gap> RequirePackage("carat"); true gap> names := []; [ ] gap> GROUPS := []; [ ] gap> R := CaratReadBravaisFile("ordnung.128/(2)^4(4)^4/group.1188"); rec( generators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 128 ) gap> P1 := Group(R.generators); gap> Append(names,["ordnung.128/(2)^4(4)^4/words.group.1188"]); gap> Append(GROUPS,[P1]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^1(4)^4(8)^1/min.242"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] , [ [ 0, -1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] ], size := 16 ) gap> P2 := Group(R.generators); gap> Append(names,["ordnung.16/(2)^1(4)^4(8)^1/words.min.242"]); gap> Append(GROUPS,[P2]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^1(4)^4(8)^1/min.243"); rec( generators := [ [ [ 0, -1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] , [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] ], size := 16 ) gap> P3 := Group(R.generators); gap> Append(names,["ordnung.16/(2)^1(4)^4(8)^1/words.min.243"]); gap> Append(GROUPS,[P3]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^2(4)^2(8)^2/group.1189"); rec( generators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ -1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] ], size := 16 ) gap> P4 := Group(R.generators); gap> Append(names,["ordnung.16/(2)^2(4)^2(8)^2/words.group.1189"]); gap> Append(GROUPS,[P4]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^2(4)^2(8)^2/group.1190"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] , [ [ 0, 1, 0, 0, 0, 0 ], [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 16 ) gap> P5 := Group(R.generators); gap> Append(names,["ordnung.16/(2)^2(4)^2(8)^2/words.group.1190"]); gap> Append(GROUPS,[P5]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^2(4)^2(8)^2/group.1191"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 0, 1, 0, 0, 0, 0 ], [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] , [ [ -1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 16 ) gap> P6 := Group(R.generators); gap> Append(names,["ordnung.16/(2)^2(4)^2(8)^2/words.group.1191"]); gap> Append(GROUPS,[P6]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^2(4)^2(8)^2/group.1192"); rec( generators := [ [ [ 0, -1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 16 ) gap> P7 := Group(R.generators); gap> Append(names,["ordnung.16/(2)^2(4)^2(8)^2/words.group.1192"]); gap> Append(GROUPS,[P7]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^2(4)^2(8)^2/group.1193"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 0, -1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] ] , size := 16 ) gap> P8 := Group(R.generators); gap> Append(names,["ordnung.16/(2)^2(4)^2(8)^2/words.group.1193"]); gap> Append(GROUPS,[P8]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^2(4)^2(8)^2/group.1194"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 0, -1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 16 ) gap> P9 := Group(R.generators); gap> Append(names,["ordnung.16/(2)^2(4)^2(8)^2/words.group.1194"]); gap> Append(GROUPS,[P9]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^2(8)^4/group.1195"); rec( generators := [ [ [ 0, -1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] , [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 16 ) gap> P10 := Group(R.generators); gap> Append(names,["ordnung.16/(2)^2(8)^4/words.group.1195"]); gap> Append(GROUPS,[P10]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^4(16)^4/group.1196"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 0, -1, 0, 0, 0, 0 ], [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] ], size := 16 ) gap> P11 := Group(R.generators); gap> Append(names,["ordnung.16/(2)^4(16)^4/words.group.1196"]); gap> Append(GROUPS,[P11]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^4(4)^2(16)^2/group.1197"); rec( generators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 16 ) gap> P12 := Group(R.generators); gap> Append(names,["ordnung.16/(2)^4(4)^2(16)^2/words.group.1197"]); gap> Append(GROUPS,[P12]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^4(4)^2(16)^2/group.1198"); rec( generators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] , [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 16 ) gap> P13 := Group(R.generators); gap> Append(names,["ordnung.16/(2)^4(4)^2(16)^2/words.group.1198"]); gap> Append(GROUPS,[P13]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^4(4)^2(16)^2/group.1199"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, -1, 0, 0, 0, 0 ], [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 16 ) gap> P14 := Group(R.generators); gap> Append(names,["ordnung.16/(2)^4(4)^2(16)^2/words.group.1199"]); gap> Append(GROUPS,[P14]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^4(4)^2(16)^2/group.1200"); rec( generators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] , [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] ] , size := 16 ) gap> P15 := Group(R.generators); gap> Append(names,["ordnung.16/(2)^4(4)^2(16)^2/words.group.1200"]); gap> Append(GROUPS,[P15]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^4(4)^2(16)^2/group.1201"); rec( generators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] , [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 16 ) gap> P16 := Group(R.generators); gap> Append(names,["ordnung.16/(2)^4(4)^2(16)^2/words.group.1201"]); gap> Append(GROUPS,[P16]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^4(4)^2(16)^2/group.1202"); rec( generators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] , [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 16 ) gap> P17 := Group(R.generators); gap> Append(names,["ordnung.16/(2)^4(4)^2(16)^2/words.group.1202"]); gap> Append(GROUPS,[P17]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^4(8)^4/group.1203"); rec( generators := [ [ [ 0, -1, 0, 0, 0, 0 ], [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] , [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] ], size := 16 ) gap> P18 := Group(R.generators); gap> Append(names,["ordnung.16/(2)^4(8)^4/words.group.1203"]); gap> Append(GROUPS,[P18]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^4(8)^4/group.1204"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] , [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] ], size := 16 ) gap> P19 := Group(R.generators); gap> Append(names,["ordnung.16/(2)^4(8)^4/words.group.1204"]); gap> Append(GROUPS,[P19]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^4(8)^4/group.1205"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ -1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] ] , size := 16 ) gap> P20 := Group(R.generators); gap> Append(names,["ordnung.16/(2)^4(8)^4/words.group.1205"]); gap> Append(GROUPS,[P20]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^4(8)^4/group.1206"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] , [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 16 ) gap> P21 := Group(R.generators); gap> Append(names,["ordnung.16/(2)^4(8)^4/words.group.1206"]); gap> Append(GROUPS,[P21]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^4(8)^4/group.1207"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 16 ) gap> P22 := Group(R.generators); gap> Append(names,["ordnung.16/(2)^4(8)^4/words.group.1207"]); gap> Append(GROUPS,[P22]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^4(8)^4/group.1208"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 16 ) gap> P23 := Group(R.generators); gap> Append(names,["ordnung.16/(2)^4(8)^4/words.group.1208"]); gap> Append(GROUPS,[P23]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^4(8)^4/min.244"); rec( generators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ -1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 16 ) gap> P24 := Group(R.generators); gap> Append(names,["ordnung.16/(2)^4(8)^4/words.min.244"]); gap> Append(GROUPS,[P24]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^4(8)^4/min.245"); rec( generators := [ [ [ 0, -1, 0, 0, 0, 0 ], [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] , [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 16 ) gap> P25 := Group(R.generators); gap> Append(names,["ordnung.16/(2)^4(8)^4/words.min.245"]); gap> Append(GROUPS,[P25]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^4(8)^4/min.246"); rec( generators := [ [ [ 0, -1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] ], size := 16 ) gap> P26 := Group(R.generators); gap> Append(names,["ordnung.16/(2)^4(8)^4/words.min.246"]); gap> Append(GROUPS,[P26]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^4(8)^4/min.247"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, -1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 16 ) gap> P27 := Group(R.generators); gap> Append(names,["ordnung.16/(2)^4(8)^4/words.min.247"]); gap> Append(GROUPS,[P27]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^1(4)^4(8)^1/group.1209"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 0, -1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 32 ) gap> P28 := Group(R.generators); gap> Append(names,["ordnung.32/(2)^1(4)^4(8)^1/words.group.1209"]); gap> Append(GROUPS,[P28]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^2(4)^2(8)^2/group.1210"); rec( generators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ -1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 32 ) gap> P29 := Group(R.generators); gap> Append(names,["ordnung.32/(2)^2(4)^2(8)^2/words.group.1210"]); gap> Append(GROUPS,[P29]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^2(4)^2(8)^2/group.1211"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 0, -1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 32 ) gap> P30 := Group(R.generators); gap> Append(names,["ordnung.32/(2)^2(4)^2(8)^2/words.group.1211"]); gap> Append(GROUPS,[P30]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^2(4)^4/group.1212"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, -1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 32 ) gap> P31 := Group(R.generators); gap> Append(names,["ordnung.32/(2)^2(4)^4/words.group.1212"]); gap> Append(GROUPS,[P31]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^2(4)^4/group.1213"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] , [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 0, -1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] ] , size := 32 ) gap> P32 := Group(R.generators); gap> Append(names,["ordnung.32/(2)^2(4)^4/words.group.1213"]); gap> Append(GROUPS,[P32]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^2(4)^4/group.1214"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 0, -1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 32 ) gap> P33 := Group(R.generators); gap> Append(names,["ordnung.32/(2)^2(4)^4/words.group.1214"]); gap> Append(GROUPS,[P33]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^2(4)^4/group.1215"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, -1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 32 ) gap> P34 := Group(R.generators); gap> Append(names,["ordnung.32/(2)^2(4)^4/words.group.1215"]); gap> Append(GROUPS,[P34]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^2(16)^2/group.1216"); rec( generators := [ [ [ 0, -1, 0, 0, 0, 0 ], [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ -1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 32 ) gap> P35 := Group(R.generators); gap> Append(names,["ordnung.32/(2)^4(4)^2(16)^2/words.group.1216"]); gap> Append(GROUPS,[P35]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^2(8)^2/group.1217"); rec( generators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] , [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 32 ) gap> P36 := Group(R.generators); gap> Append(names,["ordnung.32/(2)^4(4)^2(8)^2/words.group.1217"]); gap> Append(GROUPS,[P36]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^2(8)^2/group.1218"); rec( generators := [ [ [ 0, -1, 0, 0, 0, 0 ], [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] , [ [ -1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] , [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 32 ) gap> P37 := Group(R.generators); gap> Append(names,["ordnung.32/(2)^4(4)^2(8)^2/words.group.1218"]); gap> Append(GROUPS,[P37]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^2(8)^2/group.1219"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 0, -1, 0, 0, 0, 0 ], [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ -1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 32 ) gap> P38 := Group(R.generators); gap> Append(names,["ordnung.32/(2)^4(4)^2(8)^2/words.group.1219"]); gap> Append(GROUPS,[P38]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^2(8)^2/group.1220"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 0, -1, 0, 0, 0, 0 ], [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 32 ) gap> P39 := Group(R.generators); gap> Append(names,["ordnung.32/(2)^4(4)^2(8)^2/words.group.1220"]); gap> Append(GROUPS,[P39]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^2(8)^2/group.1221"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, -1, 0, 0, 0, 0 ], [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ -1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] ] , size := 32 ) gap> P40 := Group(R.generators); gap> Append(names,["ordnung.32/(2)^4(4)^2(8)^2/words.group.1221"]); gap> Append(GROUPS,[P40]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^2(8)^2/group.1222"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, -1, 0, 0, 0, 0 ], [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ -1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 32 ) gap> P41 := Group(R.generators); gap> Append(names,["ordnung.32/(2)^4(4)^2(8)^2/words.group.1222"]); gap> Append(GROUPS,[P41]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^2(8)^2/group.1223"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, -1, 0, 0, 0, 0 ], [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] , [ [ -1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 32 ) gap> P42 := Group(R.generators); gap> Append(names,["ordnung.32/(2)^4(4)^2(8)^2/words.group.1223"]); gap> Append(GROUPS,[P42]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^2(8)^2/group.1224"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, -1, 0, 0, 0, 0 ], [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] , [ [ -1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] ] , size := 32 ) gap> P43 := Group(R.generators); gap> Append(names,["ordnung.32/(2)^4(4)^2(8)^2/words.group.1224"]); gap> Append(GROUPS,[P43]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^2(8)^2/group.1225"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] ], size := 32 ) gap> P44 := Group(R.generators); gap> Append(names,["ordnung.32/(2)^4(4)^2(8)^2/words.group.1225"]); gap> Append(GROUPS,[P44]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^2(8)^2/group.1226"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] ], size := 32 ) gap> P45 := Group(R.generators); gap> Append(names,["ordnung.32/(2)^4(4)^2(8)^2/words.group.1226"]); gap> Append(GROUPS,[P45]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^2(8)^2/group.1227"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 32 ) gap> P46 := Group(R.generators); gap> Append(names,["ordnung.32/(2)^4(4)^2(8)^2/words.group.1227"]); gap> Append(GROUPS,[P46]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^2(8)^2/group.1228"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] ], size := 32 ) gap> P47 := Group(R.generators); gap> Append(names,["ordnung.32/(2)^4(4)^2(8)^2/words.group.1228"]); gap> Append(GROUPS,[P47]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^2(8)^2/group.1229"); rec( generators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] , [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 32 ) gap> P48 := Group(R.generators); gap> Append(names,["ordnung.32/(2)^4(4)^2(8)^2/words.group.1229"]); gap> Append(GROUPS,[P48]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^2(8)^2/group.1230"); rec( generators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] , [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 32 ) gap> P49 := Group(R.generators); gap> Append(names,["ordnung.32/(2)^4(4)^2(8)^2/words.group.1230"]); gap> Append(GROUPS,[P49]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^2(8)^2/group.1231"); rec( generators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] , [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] ] , size := 32 ) gap> P50 := Group(R.generators); gap> Append(names,["ordnung.32/(2)^4(4)^2(8)^2/words.group.1231"]); gap> Append(GROUPS,[P50]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^2(8)^2/group.1232"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 32 ) gap> P51 := Group(R.generators); gap> Append(names,["ordnung.32/(2)^4(4)^2(8)^2/words.group.1232"]); gap> Append(GROUPS,[P51]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^2(8)^2/group.1233"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] , [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 32 ) gap> P52 := Group(R.generators); gap> Append(names,["ordnung.32/(2)^4(4)^2(8)^2/words.group.1233"]); gap> Append(GROUPS,[P52]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^2(8)^2/group.1234"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] , [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 0, -1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] ] , size := 32 ) gap> P53 := Group(R.generators); gap> Append(names,["ordnung.32/(2)^4(4)^2(8)^2/words.group.1234"]); gap> Append(GROUPS,[P53]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^2(8)^2/group.1235"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 0, -1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] ] , size := 32 ) gap> P54 := Group(R.generators); gap> Append(names,["ordnung.32/(2)^4(4)^2(8)^2/words.group.1235"]); gap> Append(GROUPS,[P54]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^2(8)^2/group.1236"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 32 ) gap> P55 := Group(R.generators); gap> Append(names,["ordnung.32/(2)^4(4)^2(8)^2/words.group.1236"]); gap> Append(GROUPS,[P55]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^2(8)^2/group.1237"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] , [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 32 ) gap> P56 := Group(R.generators); gap> Append(names,["ordnung.32/(2)^4(4)^2(8)^2/words.group.1237"]); gap> Append(GROUPS,[P56]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^2(8)^2/group.1238"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 32 ) gap> P57 := Group(R.generators); gap> Append(names,["ordnung.32/(2)^4(4)^2(8)^2/words.group.1238"]); gap> Append(GROUPS,[P57]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^2(8)^2/group.1239"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] , [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] , [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] ], size := 32 ) gap> P58 := Group(R.generators); gap> Append(names,["ordnung.32/(2)^4(4)^2(8)^2/words.group.1239"]); gap> Append(GROUPS,[P58]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^2(8)^2/group.1240"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 32 ) gap> P59 := Group(R.generators); gap> Append(names,["ordnung.32/(2)^4(4)^2(8)^2/words.group.1240"]); gap> Append(GROUPS,[P59]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^2(8)^2/group.1241"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] , [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 0, -1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 32 ) gap> P60 := Group(R.generators); gap> Append(names,["ordnung.32/(2)^4(4)^2(8)^2/words.group.1241"]); gap> Append(GROUPS,[P60]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(8)^4/group.1242"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, -1, 0, 0, 0, 0 ], [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ -1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 32 ) gap> P61 := Group(R.generators); gap> Append(names,["ordnung.32/(2)^4(8)^4/words.group.1242"]); gap> Append(GROUPS,[P61]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(8)^4/group.1243"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, -1, 0, 0, 0, 0 ], [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ -1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 32 ) gap> P62 := Group(R.generators); gap> Append(names,["ordnung.32/(2)^4(8)^4/words.group.1243"]); gap> Append(GROUPS,[P62]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(8)^4/group.1244"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 0, -1, 0, 0, 0, 0 ], [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 32 ) gap> P63 := Group(R.generators); gap> Append(names,["ordnung.32/(2)^4(8)^4/words.group.1244"]); gap> Append(GROUPS,[P63]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(8)^4/group.1245"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] , [ [ 0, -1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 32 ) gap> P64 := Group(R.generators); gap> Append(names,["ordnung.32/(2)^4(8)^4/words.group.1245"]); gap> Append(GROUPS,[P64]); gap> R := CaratReadBravaisFile("ordnung.64/(2)^2(4)^4/group.1246"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, -1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 64 ) gap> P65 := Group(R.generators); gap> Append(names,["ordnung.64/(2)^2(4)^4/words.group.1246"]); gap> Append(GROUPS,[P65]); gap> R := CaratReadBravaisFile("ordnung.64/(2)^4(4)^2(8)^2/group.1247"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, -1, 0, 0, 0, 0 ], [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ -1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 64 ) gap> P66 := Group(R.generators); gap> Append(names,["ordnung.64/(2)^4(4)^2(8)^2/words.group.1247"]); gap> Append(GROUPS,[P66]); gap> R := CaratReadBravaisFile("ordnung.64/(2)^4(4)^2(8)^2/group.1248"); rec( generators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] , [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] , [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] ] , size := 64 ) gap> P67 := Group(R.generators); gap> Append(names,["ordnung.64/(2)^4(4)^2(8)^2/words.group.1248"]); gap> Append(GROUPS,[P67]); gap> R := CaratReadBravaisFile("ordnung.64/(2)^4(4)^2(8)^2/group.1249"); rec( generators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] , [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 64 ) gap> P68 := Group(R.generators); gap> Append(names,["ordnung.64/(2)^4(4)^2(8)^2/words.group.1249"]); gap> Append(GROUPS,[P68]); gap> R := CaratReadBravaisFile("ordnung.64/(2)^4(4)^2(8)^2/group.1250"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 64 ) gap> P69 := Group(R.generators); gap> Append(names,["ordnung.64/(2)^4(4)^2(8)^2/words.group.1250"]); gap> Append(GROUPS,[P69]); gap> R := CaratReadBravaisFile("ordnung.64/(2)^4(4)^2(8)^2/group.1251"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] , [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 0, -1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 64 ) gap> P70 := Group(R.generators); gap> Append(names,["ordnung.64/(2)^4(4)^2(8)^2/words.group.1251"]); gap> Append(GROUPS,[P70]); gap> R := CaratReadBravaisFile("ordnung.64/(2)^4(4)^4/group.1252"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 64 ) gap> P71 := Group(R.generators); gap> Append(names,["ordnung.64/(2)^4(4)^4/words.group.1252"]); gap> Append(GROUPS,[P71]); gap> R := CaratReadBravaisFile("ordnung.64/(2)^4(4)^4/group.1253"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] , [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] , [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] , [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] ], size := 64 ) gap> P72 := Group(R.generators); gap> Append(names,["ordnung.64/(2)^4(4)^4/words.group.1253"]); gap> Append(GROUPS,[P72]); gap> R := CaratReadBravaisFile("ordnung.64/(2)^4(4)^4/group.1254"); rec( generators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] ] , size := 64 ) gap> P73 := Group(R.generators); gap> Append(names,["ordnung.64/(2)^4(4)^4/words.group.1254"]); gap> Append(GROUPS,[P73]); gap> R := CaratReadBravaisFile("ordnung.64/(2)^4(4)^4/group.1255"); rec( generators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] , [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] ] , size := 64 ) gap> P74 := Group(R.generators); gap> Append(names,["ordnung.64/(2)^4(4)^4/words.group.1255"]); gap> Append(GROUPS,[P74]); gap> R := CaratReadBravaisFile("ordnung.64/(2)^4(4)^4/group.1256"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 64 ) gap> P75 := Group(R.generators); gap> Append(names,["ordnung.64/(2)^4(4)^4/words.group.1256"]); gap> Append(GROUPS,[P75]); gap> R := CaratReadBravaisFile("ordnung.64/(2)^4(4)^4/group.1257"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] , [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 64 ) gap> P76 := Group(R.generators); gap> Append(names,["ordnung.64/(2)^4(4)^4/words.group.1257"]); gap> Append(GROUPS,[P76]); gap> R := CaratReadBravaisFile("ordnung.8/(2)^2(8)^4/min.248"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0 ], [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 8 ) gap> P77 := Group(R.generators); gap> Append(names,["ordnung.8/(2)^2(8)^4/words.min.248"]); gap> Append(GROUPS,[P77]); gap> R := CaratReadBravaisFile("ordnung.8/(2)^4(16)^4/min.249"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, -1, 0, 0, 0, 0 ], [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 8 ) gap> P78 := Group(R.generators); gap> Append(names,["ordnung.8/(2)^4(16)^4/words.min.249"]); gap> Append(GROUPS,[P78]); gap> Print(GROUPS,"\n"); [ Group( [ [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] , [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ]), Group([ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] , [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] , [ [ 0, -1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] ]), Group([ [ [ 0, -1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] , [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] ]), Group([ [ [ 0, 1, 0, 0, 0, 0 ], [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ -1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] ]), Group([ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] , [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] , [ [ 0, 1, 0, 0, 0, 0 ], [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ]), Group([ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 0, 1, 0, 0, 0, 0 ], [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] , [ [ -1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ]), Group([ [ [ 0, -1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ] , [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 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-1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] , [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] ]), Group([ [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] ]), Group([ [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] , [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] ]), Group([ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ]), Group([ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] , [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ], [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ]), Group([ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] , [ [ 0, 1, 0, 0, 0, 0 ], [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ]), Group([ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ] , [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ], [ [ 0, -1, 0, 0, 0, 0 ], [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ]) ] gap> Print(names,"\n"); [ "ordnung.128/(2)^4(4)^4/words.group.1188", "ordnung.16/(2)^1(4)^4(8)^1/words.min.242", "ordnung.16/(2)^1(4)^4(8)^1/words.min.243", "ordnung.16/(2)^2(4)^2(8)^2/words.group.1189", "ordnung.16/(2)^2(4)^2(8)^2/words.group.1190", "ordnung.16/(2)^2(4)^2(8)^2/words.group.1191", "ordnung.16/(2)^2(4)^2(8)^2/words.group.1192", "ordnung.16/(2)^2(4)^2(8)^2/words.group.1193", "ordnung.16/(2)^2(4)^2(8)^2/words.group.1194", "ordnung.16/(2)^2(8)^4/words.group.1195", "ordnung.16/(2)^4(16)^4/words.group.1196", "ordnung.16/(2)^4(4)^2(16)^2/words.group.1197", "ordnung.16/(2)^4(4)^2(16)^2/words.group.1198", "ordnung.16/(2)^4(4)^2(16)^2/words.group.1199", "ordnung.16/(2)^4(4)^2(16)^2/words.group.1200", "ordnung.16/(2)^4(4)^2(16)^2/words.group.1201", "ordnung.16/(2)^4(4)^2(16)^2/words.group.1202", "ordnung.16/(2)^4(8)^4/words.group.1203", "ordnung.16/(2)^4(8)^4/words.group.1204", "ordnung.16/(2)^4(8)^4/words.group.1205", "ordnung.16/(2)^4(8)^4/words.group.1206", "ordnung.16/(2)^4(8)^4/words.group.1207", "ordnung.16/(2)^4(8)^4/words.group.1208", "ordnung.16/(2)^4(8)^4/words.min.244", "ordnung.16/(2)^4(8)^4/words.min.245" , "ordnung.16/(2)^4(8)^4/words.min.246", "ordnung.16/(2)^4(8)^4/words.min.247", "ordnung.32/(2)^1(4)^4(8)^1/words.group.1209", "ordnung.32/(2)^2(4)^2(8)^2/words.group.1210", "ordnung.32/(2)^2(4)^2(8)^2/words.group.1211", "ordnung.32/(2)^2(4)^4/words.group.1212", "ordnung.32/(2)^2(4)^4/words.group.1213", "ordnung.32/(2)^2(4)^4/words.group.1214", "ordnung.32/(2)^2(4)^4/words.group.1215", "ordnung.32/(2)^4(4)^2(16)^2/words.group.1216", "ordnung.32/(2)^4(4)^2(8)^2/words.group.1217", "ordnung.32/(2)^4(4)^2(8)^2/words.group.1218", "ordnung.32/(2)^4(4)^2(8)^2/words.group.1219", "ordnung.32/(2)^4(4)^2(8)^2/words.group.1220", "ordnung.32/(2)^4(4)^2(8)^2/words.group.1221", "ordnung.32/(2)^4(4)^2(8)^2/words.group.1222", "ordnung.32/(2)^4(4)^2(8)^2/words.group.1223", "ordnung.32/(2)^4(4)^2(8)^2/words.group.1224", "ordnung.32/(2)^4(4)^2(8)^2/words.group.1225", "ordnung.32/(2)^4(4)^2(8)^2/words.group.1226", "ordnung.32/(2)^4(4)^2(8)^2/words.group.1227", "ordnung.32/(2)^4(4)^2(8)^2/words.group.1228", "ordnung.32/(2)^4(4)^2(8)^2/words.group.1229", "ordnung.32/(2)^4(4)^2(8)^2/words.group.1230", "ordnung.32/(2)^4(4)^2(8)^2/words.group.1231", "ordnung.32/(2)^4(4)^2(8)^2/words.group.1232", "ordnung.32/(2)^4(4)^2(8)^2/words.group.1233", "ordnung.32/(2)^4(4)^2(8)^2/words.group.1234", "ordnung.32/(2)^4(4)^2(8)^2/words.group.1235", "ordnung.32/(2)^4(4)^2(8)^2/words.group.1236", "ordnung.32/(2)^4(4)^2(8)^2/words.group.1237", "ordnung.32/(2)^4(4)^2(8)^2/words.group.1238", "ordnung.32/(2)^4(4)^2(8)^2/words.group.1239", "ordnung.32/(2)^4(4)^2(8)^2/words.group.1240", "ordnung.32/(2)^4(4)^2(8)^2/words.group.1241", "ordnung.32/(2)^4(8)^4/words.group.1242", "ordnung.32/(2)^4(8)^4/words.group.1243", "ordnung.32/(2)^4(8)^4/words.group.1244", "ordnung.32/(2)^4(8)^4/words.group.1245", "ordnung.64/(2)^2(4)^4/words.group.1246", "ordnung.64/(2)^4(4)^2(8)^2/words.group.1247", "ordnung.64/(2)^4(4)^2(8)^2/words.group.1248", "ordnung.64/(2)^4(4)^2(8)^2/words.group.1249", "ordnung.64/(2)^4(4)^2(8)^2/words.group.1250", "ordnung.64/(2)^4(4)^2(8)^2/words.group.1251", "ordnung.64/(2)^4(4)^4/words.group.1252", "ordnung.64/(2)^4(4)^4/words.group.1253", "ordnung.64/(2)^4(4)^4/words.group.1254", "ordnung.64/(2)^4(4)^4/words.group.1255", "ordnung.64/(2)^4(4)^4/words.group.1256", "ordnung.64/(2)^4(4)^4/words.group.1257", "ordnung.8/(2)^2(8)^4/words.min.248", "ordnung.8/(2)^4(16)^4/words.min.249" ] gap> Size(GROUPS); 78 gap> Size(names); 78 gap> Read("../../TGROUPS.GAP"); gap> for i in [1..Size(GROUPS)] do > SubgroupWords(GROUPS[i], names[i]); > od; [ x4*x6, x5, x5*x1*x5, x2, x3, x1*x5*x1*x5 ] [ x4*x6, x5, x5*x1*x5, x2, x4, x1*x5*x1*x5 ] [ x4*x6, x5, x5*x1*x5, x2, x3*x4, x1*x5*x1*x5 ] [ x4*x6, x5, x5*x1*x5, x3, x4, x1*x5*x1*x5 ] [ x4*x6, x5, x5*x1*x5, x2*x4, x3, x1*x5*x1*x5 ] [ x4*x6, x5, x5*x1*x5, x2*x3, x4, x1*x5*x1*x5 ] [ x4*x6, x5, x5*x1*x5, x2*x4, x3*x4, x1*x5*x1*x5 ] [ x4*x6, x5, x2, x3, x4, x1*x5*x1*x5 ] [ x4*x6, x5, x4*x5*x1*x5, x2, x3, x1*x5*x1*x5 ] [ x4*x6, x5, x3*x5*x1*x5, x2, x4, x1*x5*x1*x5 ] [ x4*x6, x5, x4*x5*x1*x5, x2, x3*x4, x1*x5*x1*x5 ] [ x4*x6, x5, x2*x5*x1*x5, x3, x4, x1*x5*x1*x5 ] [ x4*x6, x5, x4*x5*x1*x5, x2*x4, x3, x1*x5*x1*x5 ] [ x4*x6, x5, x3*x5*x1*x5, x2*x3, x4, x1*x5*x1*x5 ] [ x4*x6, x5, x4*x5*x1*x5, x2*x4, x3*x4, x1*x5*x1*x5 ] [ x4*x6, x5*x1*x5, x2, x3, x4, x1*x5*x1*x5 ] [ x4*x6, x4*x5, x5*x1*x5, x2, x3, x1*x5*x1*x5 ] [ x4*x6, x3*x5, x5*x1*x5, x2, x4, x1*x5*x1*x5 ] [ x4*x6, x4*x5, x5*x1*x5, x2, x3*x4, x1*x5*x1*x5 ] [ x4*x6, x2*x5, x5*x1*x5, x3, x4, x1*x5*x1*x5 ] [ x4*x6, x4*x5, x5*x1*x5, x2*x4, x3, x1*x5*x1*x5 ] [ x4*x6, x3*x5, x5*x1*x5, x2*x3, x4, x1*x5*x1*x5 ] [ x4*x6, x4*x5, x5*x1*x5, x2*x4, x3*x4, x1*x5*x1*x5 ] [ x4*x6, x1*x5, x2, x3, x4, x1*x5*x1*x5 ] [ x4*x6, x4*x5, x4*x5*x1*x5, x2, x3, x1*x5*x1*x5 ] [ x4*x6, x3*x5, x3*x5*x1*x5, x2, x4, x1*x5*x1*x5 ] [ x4*x6, x4*x5, x4*x5*x1*x5, x2, x3*x4, x1*x5*x1*x5 ] [ x4*x6, x2*x5, x2*x5*x1*x5, x3, x4, x1*x5*x1*x5 ] [ x4*x6, x4*x5, x4*x5*x1*x5, x2*x4, x3, x1*x5*x1*x5 ] [ x4*x6, x3*x5, x3*x5*x1*x5, x2*x3, x4, x1*x5*x1*x5 ] [ x4*x6, x4*x5, x4*x5*x1*x5, x2*x4, x3*x4, x1*x5*x1*x5 ] [ x5, x5*x1*x5, x2, x3, x4, x1*x5*x1*x5 ] [ x6, x5, x5*x1*x5, x2, x3, x1*x5*x1*x5 ] [ x3*x4*x6, x5, x5*x1*x5, x2, x4, x1*x5*x1*x5 ] [ x6, x5, x5*x1*x5, x2, x3*x4, x1*x5*x1*x5 ] [ x2*x4*x6, x5, x5*x1*x5, x3, x4, x1*x5*x1*x5 ] [ x6, x5, x5*x1*x5, x2*x4, x3, x1*x5*x1*x5 ] [ x3*x4*x6, x5, x5*x1*x5, x2*x3, x4, x1*x5*x1*x5 ] [ x6, x5, x5*x1*x5, x2*x4, x3*x4, x1*x5*x1*x5 ] [ x4*x5*x1*x5*x6, x5, x2, x3, x4, x1*x5*x1*x5 ] [ x6, x5, x4*x5*x1*x5, x2, x3, x1*x5*x1*x5 ] [ x3*x4*x6, x5, x3*x5*x1*x5, x2, x4, x1*x5*x1*x5 ] [ x6, x5, x4*x5*x1*x5, x2, x3*x4, x1*x5*x1*x5 ] [ x2*x4*x6, x5, x2*x5*x1*x5, x3, x4, x1*x5*x1*x5 ] [ x6, x5, x4*x5*x1*x5, x2*x4, x3, x1*x5*x1*x5 ] [ x3*x4*x6, x5, x3*x5*x1*x5, x2*x3, x4, x1*x5*x1*x5 ] [ x6, x5, x4*x5*x1*x5, x2*x4, x3*x4, x1*x5*x1*x5 ] [ x4*x5*x6, x5*x1*x5, x2, x3, x4, x1*x5*x1*x5 ] [ x6, x4*x5, x5*x1*x5, x2, x3, x1*x5*x1*x5 ] [ x3*x4*x6, x3*x5, x5*x1*x5, x2, x4, x1*x5*x1*x5 ] [ x6, x4*x5, x5*x1*x5, x2, x3*x4, x1*x5*x1*x5 ] [ x2*x4*x6, x2*x5, x5*x1*x5, x3, x4, x1*x5*x1*x5 ] [ x6, x4*x5, x5*x1*x5, x2*x4, x3, x1*x5*x1*x5 ] [ x3*x4*x6, x3*x5, x5*x1*x5, x2*x3, x4, x1*x5*x1*x5 ] [ x6, x4*x5, x5*x1*x5, x2*x4, x3*x4, x1*x5*x1*x5 ] [ x4*x5*x1*x5*x6, x1*x5, x2, x3, x4, x1*x5*x1*x5 ] [ x6, x4*x5, x4*x5*x1*x5, x2, x3, x1*x5*x1*x5 ] [ x3*x4*x6, x3*x5, x3*x5*x1*x5, x2, x4, x1*x5*x1*x5 ] [ x6, x4*x5, x4*x5*x1*x5, x2, x3*x4, x1*x5*x1*x5 ] [ x2*x4*x6, x2*x5, x2*x5*x1*x5, x3, x4, x1*x5*x1*x5 ] [ x6, x4*x5, x4*x5*x1*x5, x2*x4, x3, x1*x5*x1*x5 ] [ x3*x4*x6, x3*x5, x3*x5*x1*x5, x2*x3, x4, x1*x5*x1*x5 ] [ x6, x4*x5, x4*x5*x1*x5, x2*x4, x3*x4, x1*x5*x1*x5 ] [ x1*x2*x3, x2, x3^2 ] [ x1*x2*x3, x1, x3^2 ] [ x1*x2*x3, x1*x2, x3^2 ] [ x2, x1, x3^2 ] [ x2*x3, x2, x3^2 ] [ x1*x3, x1, x3^2 ] [ x2*x3, x1*x2, x3^2 ] [ x2*x3, x2, x1^2 ] [ x2*x3, x1, x1^2 ] [ x2*x3, x1*x2, x1^2 ] [ x2, x1, x1^2 ] [ x1*x2*x3, x2, x1^2 ] [ x3, x1, x1^2 ] [ x1*x2*x3, x1*x2, x1^2 ] [ x1^2*x2*x3, x2, x1^2 ] [ x1^2*x2*x3, x1, x1^2 ] [ x1^2*x2*x3, x1*x2, x1^2 ] [ x2, x1, x1^2 ] [ x1^3*x2*x3, x2, x1^2 ] [ x1^2*x3, x1, x1^2 ] [ x1^3*x2*x3, x1*x2, x1^2 ] [ x3, x1*x2, x3^2 ] [ x3, x1, x3^2 ] [ x3, x2, x3^2 ] [ x1*x2, x1, x3^2 ] [ x1*x3, x1*x2, x3^2 ] [ x1*x2*x3, x1, x3^2 ] [ x1*x3, x2, x3^2 ] [ x2^2*x3, x2, x2^2 ] [ x2^2*x3, x1, x2^2 ] [ x2^2*x3, x1*x2, x2^2 ] [ x2, x1, x2^2 ] [ x1*x2^2*x3, x2, x2^2 ] [ x2^3*x3, x1, x2^2 ] [ x1*x2^2*x3, x1*x2, x2^2 ] [ x3, x2, x1^2 ] [ x3, x1, x1^2 ] [ x3, x1*x2, x1^2 ] [ x2, x1, x1^2 ] [ x1*x3, x2, x1^2 ] [ x2*x3, x1, x1^2 ] [ x1*x3, x1*x2, x1^2 ] [ x3, x2, x3^2 ] [ x3, x1, x3^2 ] [ x3, x1*x2, x3^2 ] [ x2, x1, x3^2 ] [ x1*x3, x2, x3^2 ] [ x2*x3, x1, x3^2 ] [ x1*x3, x1*x2, x3^2 ] [ x3, x2, x3^2 ] [ x3, x1, x3^2 ] [ x3, x1*x2, x3^2 ] [ x2, x1, x3^2 ] [ x1*x3, x2, x3^2 ] [ x2*x3, x1, x3^2 ] [ x1*x3, x1*x2, x3^2 ] [ x2*x3, x2, x1^2 ] [ x2*x3, x1, x1^2 ] [ x2*x3, x1*x2, x1^2 ] [ x2, x1, x1^2 ] [ x1*x2*x3, x2, x1^2 ] [ x3, x1, x1^2 ] [ x1*x2*x3, x1*x2, x1^2 ] [ x3, x1, x1*x3*x1*x3 ] [ x3, x2, x1*x3*x1*x3 ] [ x3, x1*x2, x1*x3*x1*x3 ] [ x1, x2, x1*x3*x1*x3 ] [ x2*x3, x1, x1*x3*x1*x3 ] [ x3*x1, x2, x1*x3*x1*x3 ] [ x2*x3, x1*x2, x1*x3*x1*x3 ] [ x3, x2, x1*x2*x1*x2 ] [ x3, x2*x1*x2, x1*x2*x1*x2 ] [ x3, x1*x2, x1*x2*x1*x2 ] [ x2, x2*x1*x2, x1*x2*x1*x2 ] [ x2*x1*x2*x3, x2, x1*x2*x1*x2 ] [ x2*x3, x2*x1*x2, x1*x2*x1*x2 ] [ x2*x1*x2*x3, x1*x2, x1*x2*x1*x2 ] [ x3, x2, x1*x2*x1*x2 ] [ x3, x2*x1*x2, x1*x2*x1*x2 ] [ x3, x1*x2, x1*x2*x1*x2 ] [ x2, x2*x1*x2, x1*x2*x1*x2 ] [ x2*x1*x2*x3, x2, x1*x2*x1*x2 ] [ x2*x3, x2*x1*x2, x1*x2*x1*x2 ] [ x2*x1*x2*x3, x1*x2, x1*x2*x1*x2 ] [ x3, x2, x1*x2*x1*x2 ] [ x3, x1, x1*x2*x1*x2 ] [ x3, x2*x1, x1*x2*x1*x2 ] [ x2, x1, x1*x2*x1*x2 ] [ x1*x3, x2, x1*x2*x1*x2 ] [ x2*x3, x1, x1*x2*x1*x2 ] [ x1*x3, x2*x1, x1*x2*x1*x2 ] [ x2*x3, x3*x1*x3, x1*x3*x1*x3 ] [ x2*x3, x2, x1*x3*x1*x3 ] [ x2*x3, x2*x3*x1*x3, x1*x3*x1*x3 ] [ x3*x1*x3, x2, x1*x3*x1*x3 ] [ x3, x3*x1*x3, x1*x3*x1*x3 ] [ x1*x2*x3, x2, x1*x3*x1*x3 ] [ x3, x2*x3*x1*x3, x1*x3*x1*x3 ] [ x2*x3, x3*x1*x3, x1*x3*x1*x3 ] [ x2*x3, x2, x1*x3*x1*x3 ] [ x2*x3, x2*x3*x1*x3, x1*x3*x1*x3 ] [ x3*x1*x3, x2, x1*x3*x1*x3 ] [ x3, x3*x1*x3, x1*x3*x1*x3 ] [ x1*x2*x3, x2, x1*x3*x1*x3 ] [ x3, x2*x3*x1*x3, x1*x3*x1*x3 ] [ x2*x3, x3*x1*x3, x1*x3*x1*x3 ] [ x2*x3, x2, x1*x3*x1*x3 ] [ x2*x3, x2*x3*x1*x3, x1*x3*x1*x3 ] [ x3*x1*x3, x2, x1*x3*x1*x3 ] [ x3, x3*x1*x3, x1*x3*x1*x3 ] [ x1*x2*x3, x2, x1*x3*x1*x3 ] [ x3, x2*x3*x1*x3, x1*x3*x1*x3 ] [ x2*x3, x3*x1*x3, x1*x3*x1*x3 ] [ x2*x3, x2, x1*x3*x1*x3 ] [ x2*x3, x2*x3*x1*x3, x1*x3*x1*x3 ] [ x3*x1*x3, x2, x1*x3*x1*x3 ] [ x3, x3*x1*x3, x1*x3*x1*x3 ] [ x1*x2*x3, x2, x1*x3*x1*x3 ] [ x3, x2*x3*x1*x3, x1*x3*x1*x3 ] [ x3, x1, x1*x3*x1*x3 ] [ x3, x2, x1*x3*x1*x3 ] [ x3, x1*x2, x1*x3*x1*x3 ] [ x1, x2, x1*x3*x1*x3 ] [ x2*x3, x1, x1*x3*x1*x3 ] [ x3*x1, x2, x1*x3*x1*x3 ] [ x2*x3, x1*x2, x1*x3*x1*x3 ] [ x2*x3*x2, x1, x2*x3*x2*x3 ] [ x2*x3*x2, x1*x3*x2*x3, x2*x3*x2*x3 ] [ x2*x3*x2, x3*x2*x3, x2*x3*x2*x3 ] [ x1, x1*x3*x2*x3, x2*x3*x2*x3 ] [ x1*x3*x2, x1, x2*x3*x2*x3 ] [ x1*x2*x3*x2, x1*x3*x2*x3, x2*x3*x2*x3 ] [ x1*x3*x2, x3*x2*x3, x2*x3*x2*x3 ] [ x3, x1, x2*x3*x2*x3 ] [ x3, x1*x2, x2*x3*x2*x3 ] [ x3, x2, x2*x3*x2*x3 ] [ x1, x1*x2, x2*x3*x2*x3 ] [ x1*x3*x2, x1, x2*x3*x2*x3 ] [ x1*x3, x1*x2, x2*x3*x2*x3 ] [ x1*x3*x2, x2, x2*x3*x2*x3 ] [ x3, x1, x2*x3*x2*x3 ] [ x3, x1*x2, x2*x3*x2*x3 ] [ x3, x2, x2*x3*x2*x3 ] [ x1, x1*x2, x2*x3*x2*x3 ] [ x1*x3*x2, x1, x2*x3*x2*x3 ] [ x1*x3, x1*x2, x2*x3*x2*x3 ] [ x1*x3*x2, x2, x2*x3*x2*x3 ] [ x3, x1, x2*x3*x2*x3 ] [ x3, x1*x2, x2*x3*x2*x3 ] [ x3, x2, x2*x3*x2*x3 ] [ x1, x1*x2, x2*x3*x2*x3 ] [ x1*x3*x2, x1, x2*x3*x2*x3 ] [ x1*x3, x1*x2, x2*x3*x2*x3 ] [ x1*x3*x2, x2, x2*x3*x2*x3 ] [ x3, x1*x2*x1, x1*x2*x1*x2 ] [ x3, x2*x1*x2, x1*x2*x1*x2 ] [ x3, x2*x1, x1*x2*x1*x2 ] [ x1*x2*x1, x2*x1*x2, x1*x2*x1*x2 ] [ x2*x1*x2*x3, x1*x2*x1, x1*x2*x1*x2 ] [ x1*x2*x1*x3, x2*x1*x2, x1*x2*x1*x2 ] [ x2*x1*x2*x3, x2*x1, x1*x2*x1*x2 ] [ x3, x2, x1*x2*x1*x2 ] [ x3, x2*x1*x2, x1*x2*x1*x2 ] [ x3, x1*x2, x1*x2*x1*x2 ] [ x2, x2*x1*x2, x1*x2*x1*x2 ] [ x2*x1*x2*x3, x2, x1*x2*x1*x2 ] [ x2*x3, x2*x1*x2, x1*x2*x1*x2 ] [ x2*x1*x2*x3, x1*x2, x1*x2*x1*x2 ] [ x3, x1, x1^2 ] [ x3, x2, x1^2 ] [ x3, x1*x2, x1^2 ] [ x1, x2, x1^2 ] [ x2*x3, x1, x1^2 ] [ x1^3*x3, x2, x1^2 ] [ x2*x3, x1*x2, x1^2 ] [ x3, x1, x3^2 ] [ x3, x2, x3^2 ] [ x3, x1*x2, x3^2 ] [ x1, x2, x3^2 ] [ x3*x2, x1, x3^2 ] [ x1*x3, x2, x3^2 ] [ x3*x2, x1*x2, x3^2 ] [ x4, x3, x2, x3^2 ] [ x4, x3, x1, x3^2 ] [ x4, x3, x1*x2, x3^2 ] [ x4, x2, x1, x3^2 ] [ x4, x1*x3, x2, x3^2 ] [ x4, x2*x3, x1, x3^2 ] [ x4, x1*x3, x1*x2, x3^2 ] [ x3, x2, x1, x3^2 ] [ x1*x4, x3, x2, x3^2 ] [ x2*x4, x3, x1, x3^2 ] [ x1*x4, x3, x1*x2, x3^2 ] [ x3*x4, x2, x1, x3^2 ] [ x1*x4, x1*x3, x2, x3^2 ] [ x2*x4, x2*x3, x1, x3^2 ] [ x1*x4, x1*x3, x1*x2, x3^2 ] [ x2*x4, x1^2*x3, x2, x1^2 ] [ x2*x4, x1^2*x3, x1, x1^2 ] [ x2*x4, x1^2*x3, x1*x2, x1^2 ] [ x2*x4, x2, x1, x1^2 ] [ x2*x4, x1^3*x3, x2, x1^2 ] [ x2*x4, x1^2*x2*x3, x1, x1^2 ] [ x2*x4, x1^3*x3, x1*x2, x1^2 ] [ x1^2*x3, x2, x1, x1^2 ] [ x1*x2*x4, x1^2*x3, x2, x1^2 ] [ x4, x1^2*x3, x1, x1^2 ] [ x1*x2*x4, x1^2*x3, x1*x2, x1^2 ] [ x1^2*x2*x3*x4, x2, x1, x1^2 ] [ x1*x2*x4, x1^3*x3, x2, x1^2 ] [ x4, x1^2*x2*x3, x1, x1^2 ] [ x1*x2*x4, x1^3*x3, x1*x2, x1^2 ] [ x4, x1*x3, x2, x2^2 ] [ x4, x1*x3, x1, x2^2 ] [ x4, x1*x3, x1*x2, x2^2 ] [ x4, x2, x1, x2^2 ] [ x4, x3, x2, x2^2 ] [ x4, x1*x2*x3, x1, x2^2 ] [ x4, x3, x1*x2, x2^2 ] [ x1*x3, x2, x1, x2^2 ] [ x1*x4, x1*x3, x2, x2^2 ] [ x2*x4, x1*x3, x1, x2^2 ] [ x1*x4, x1*x3, x1*x2, x2^2 ] [ x1*x3*x4, x2, x1, x2^2 ] [ x1*x4, x3, x2, x2^2 ] [ x2*x4, x1*x2*x3, x1, x2^2 ] [ x1*x4, x3, x1*x2, x2^2 ] [ x4, x3, x2, x3^2 ] [ x4, x3, x1, x3^2 ] [ x4, x3, x1*x2, x3^2 ] [ x4, x2, x1, x3^2 ] [ x4, x1*x3, x2, x3^2 ] [ x4, x2*x3, x1, x3^2 ] [ x4, x1*x3, x1*x2, x3^2 ] [ x3, x2, x1, x3^2 ] [ x1*x4, x3, x2, x3^2 ] [ x2*x4, x3, x1, x3^2 ] [ x1*x4, x3, x1*x2, x3^2 ] [ x3*x4, x2, x1, x3^2 ] [ x1*x4, x1*x3, x2, x3^2 ] [ x2*x4, x2*x3, x1, x3^2 ] [ x1*x4, x1*x3, x1*x2, x3^2 ] [ x4, x3, x2, x4^2 ] [ x4, x3, x1, x4^2 ] [ x4, x3, x1*x2, x4^2 ] [ x4, x2, x1, x4^2 ] [ x4, x1*x3, x2, x4^2 ] [ x4, x2*x3, x1, x4^2 ] [ x4, x1*x3, x1*x2, x4^2 ] [ x3, x2, x1, x4^2 ] [ x1*x4, x3, x2, x4^2 ] [ x2*x4, x3, x1, x4^2 ] [ x1*x4, x3, x1*x2, x4^2 ] [ x3*x4, x2, x1, x4^2 ] [ x1*x4, x1*x3, x2, x4^2 ] [ x2*x4, x2*x3, x1, x4^2 ] [ x1*x4, x1*x3, x1*x2, x4^2 ] [ x3*x4, x3, x2, x4^2 ] [ x3*x4, x3, x1, x4^2 ] [ x3*x4, x3, x1*x2, x4^2 ] [ x3*x4, x2, x1, x4^2 ] [ x3*x4, x1*x3, x2, x4^2 ] [ x3*x4, x2*x3, x1, x4^2 ] [ x3*x4, x1*x3, x1*x2, x4^2 ] [ x3, x2, x1, x4^2 ] [ x1*x3*x4, x3, x2, x4^2 ] [ x2*x3*x4, x3, x1, x4^2 ] [ x1*x3*x4, x3, x1*x2, x4^2 ] [ x4, x2, x1, x4^2 ] [ x1*x3*x4, x1*x3, x2, x4^2 ] [ x2*x3*x4, x2*x3, x1, x4^2 ] [ x1*x3*x4, x1*x3, x1*x2, x4^2 ] [ x4, x3, x2, x4^2 ] [ x4, x3, x1, x4^2 ] [ x4, x3, x1*x2, x4^2 ] [ x4, x2, x1, x4^2 ] [ x4, x1*x3, x2, x4^2 ] [ x4, x2*x3, x1, x4^2 ] [ x4, x1*x3, x1*x2, x4^2 ] [ x3, x2, x1, x4^2 ] [ x1*x4, x3, x2, x4^2 ] [ x2*x4, x3, x1, x4^2 ] [ x1*x4, x3, x1*x2, x4^2 ] [ x3*x4, x2, x1, x4^2 ] [ x1*x4, x1*x3, x2, x4^2 ] [ x2*x4, x2*x3, x1, x4^2 ] [ x1*x4, x1*x3, x1*x2, x4^2 ] [ x1*x2*x3*x1*x3*x4, x3, x3*x1*x3, x1*x3*x1*x3 ] [ x1*x2*x3*x1*x3*x4, x3, x2, x1*x3*x1*x3 ] [ x1*x2*x3*x1*x3*x4, x3, x2*x3*x1*x3, x1*x3*x1*x3 ] [ x1*x2*x3*x1*x3*x4, x3*x1*x3, x2, x1*x3*x1*x3 ] [ x1*x2*x3*x1*x3*x4, x2*x3, x3*x1*x3, x1*x3*x1*x3 ] [ x1*x2*x3*x1*x3*x4, x1*x3, x2, x1*x3*x1*x3 ] [ x1*x2*x3*x1*x3*x4, x2*x3, x2*x3*x1*x3, x1*x3*x1*x3 ] [ x3, x3*x1*x3, x2, x1*x3*x1*x3 ] [ x1*x3*x1*x3*x4, x3, x3*x1*x3, x1*x3*x1*x3 ] [ x1*x2*x4, x3, x2, x1*x3*x1*x3 ] [ x1*x3*x1*x3*x4, x3, x2*x3*x1*x3, x1*x3*x1*x3 ] [ x1*x2*x3*x1*x4, x3*x1*x3, x2, x1*x3*x1*x3 ] [ x1*x3*x1*x3*x4, x2*x3, x3*x1*x3, x1*x3*x1*x3 ] [ x1*x2*x4, x1*x3, x2, x1*x3*x1*x3 ] [ x1*x3*x1*x3*x4, x2*x3, x2*x3*x1*x3, x1*x3*x1*x3 ] [ x4, x2*x3, x3*x1*x3, x1*x3*x1*x3 ] [ x4, x2*x3, x2, x1*x3*x1*x3 ] [ x4, x2*x3, x2*x3*x1*x3, x1*x3*x1*x3 ] [ x4, x3*x1*x3, x2, x1*x3*x1*x3 ] [ x4, x3, x3*x1*x3, x1*x3*x1*x3 ] [ x4, x1*x2*x3, x2, x1*x3*x1*x3 ] [ x4, x3, x2*x3*x1*x3, x1*x3*x1*x3 ] [ x2*x3, x3*x1*x3, x2, x1*x3*x1*x3 ] [ x2*x4, x2*x3, x3*x1*x3, x1*x3*x1*x3 ] [ x3*x1*x3*x4, x2*x3, x2, x1*x3*x1*x3 ] [ x2*x4, x2*x3, x2*x3*x1*x3, x1*x3*x1*x3 ] [ x2*x3*x4, x3*x1*x3, x2, x1*x3*x1*x3 ] [ x2*x4, x3, x3*x1*x3, x1*x3*x1*x3 ] [ x3*x1*x3*x4, x1*x2*x3, x2, x1*x3*x1*x3 ] [ x2*x4, x3, x2*x3*x1*x3, x1*x3*x1*x3 ] [ x4, x1*x2*x1*x2*x3, x2, x1*x2*x1*x2 ] [ x4, x1*x2*x1*x2*x3, x2*x1*x2, x1*x2*x1*x2 ] [ x4, x1*x2*x1*x2*x3, x1*x2, x1*x2*x1*x2 ] [ x4, x2, x2*x1*x2, x1*x2*x1*x2 ] [ x4, x1*x3, x2, x1*x2*x1*x2 ] [ x4, x1*x2*x1*x3, x2*x1*x2, x1*x2*x1*x2 ] [ x4, x1*x3, x1*x2, x1*x2*x1*x2 ] [ x1*x2*x1*x2*x3, x2, x2*x1*x2, x1*x2*x1*x2 ] [ x2*x1*x2*x4, x1*x2*x1*x2*x3, x2, x1*x2*x1*x2 ] [ x2*x4, x1*x2*x1*x2*x3, x2*x1*x2, x1*x2*x1*x2 ] [ x2*x1*x2*x4, x1*x2*x1*x2*x3, x1*x2, x1*x2*x1*x2 ] [ x1*x2*x1*x2*x3*x4, x2, x2*x1*x2, x1*x2*x1*x2 ] [ x2*x1*x2*x4, x1*x3, x2, x1*x2*x1*x2 ] [ x2*x4, x1*x2*x1*x3, x2*x1*x2, x1*x2*x1*x2 ] [ x2*x1*x2*x4, x1*x3, x1*x2, x1*x2*x1*x2 ] [ x1*x4, x2*x3*x2, x1, x2*x3*x2*x3 ] [ x1*x4, x2*x3*x2, x3*x2*x3, x2*x3*x2*x3 ] [ x1*x4, x2*x3*x2, x1*x3*x2*x3, x2*x3*x2*x3 ] [ x1*x4, x1, x3*x2*x3, x2*x3*x2*x3 ] [ x1*x4, x3*x2, x1, x2*x3*x2*x3 ] [ x1*x4, x1*x2*x3*x2, x3*x2*x3, x2*x3*x2*x3 ] [ x1*x4, x3*x2, x1*x3*x2*x3, x2*x3*x2*x3 ] [ x2*x3*x2, x1, x3*x2*x3, x2*x3*x2*x3 ] [ x1*x3*x2*x3*x4, x2*x3*x2, x1, x2*x3*x2*x3 ] [ x4, x2*x3*x2, x3*x2*x3, x2*x3*x2*x3 ] [ x1*x3*x2*x3*x4, x2*x3*x2, x1*x3*x2*x3, x2*x3*x2*x3 ] [ x1*x2*x3*x2*x4, x1, x3*x2*x3, x2*x3*x2*x3 ] [ x1*x3*x2*x3*x4, x3*x2, x1, x2*x3*x2*x3 ] [ x4, x1*x2*x3*x2, x3*x2*x3, x2*x3*x2*x3 ] [ x1*x3*x2*x3*x4, x3*x2, x1*x3*x2*x3, x2*x3*x2*x3 ] [ x1*x4, x3, x1, x2*x3*x2*x3 ] [ x1*x4, x3, x3*x2*x3, x2*x3*x2*x3 ] [ x1*x4, x3, x1*x3*x2*x3, x2*x3*x2*x3 ] [ x1*x4, x1, x3*x2*x3, x2*x3*x2*x3 ] [ x1*x4, x2*x3, x1, x2*x3*x2*x3 ] [ x1*x4, x1*x3, x3*x2*x3, x2*x3*x2*x3 ] [ x1*x4, x2*x3, x1*x3*x2*x3, x2*x3*x2*x3 ] [ x3, x1, x3*x2*x3, x2*x3*x2*x3 ] [ x1*x3*x2*x3*x4, x3, x1, x2*x3*x2*x3 ] [ x4, x3, x3*x2*x3, x2*x3*x2*x3 ] [ x1*x3*x2*x3*x4, x3, x1*x3*x2*x3, x2*x3*x2*x3 ] [ x1*x3*x4, x1, x3*x2*x3, x2*x3*x2*x3 ] [ x1*x3*x2*x3*x4, x2*x3, x1, x2*x3*x2*x3 ] [ x4, x1*x3, x3*x2*x3, x2*x3*x2*x3 ] [ x1*x3*x2*x3*x4, x2*x3, x1*x3*x2*x3, x2*x3*x2*x3 ] [ x3*x4*x3, x1, x2, x3*x4*x3*x4 ] [ x3*x4*x3, x1, x2*x4*x3*x4, x3*x4*x3*x4 ] [ x3*x4*x3, x1, x4*x3*x4, x3*x4*x3*x4 ] [ x3*x4*x3, x2, x2*x4*x3*x4, x3*x4*x3*x4 ] [ x3*x4*x3, x1*x2*x4*x3*x4, x2, x3*x4*x3*x4 ] [ x3*x4*x3, x1*x2, x2*x4*x3*x4, x3*x4*x3*x4 ] [ x3*x4*x3, x1*x2*x4*x3*x4, x4*x3*x4, x3*x4*x3*x4 ] [ x1, x2, x2*x4*x3*x4, x3*x4*x3*x4 ] [ x2*x4*x3, x1, x2, x3*x4*x3*x4 ] [ x2*x3*x4*x3, x1, x2*x4*x3*x4, x3*x4*x3*x4 ] [ x2*x4*x3, x1, x4*x3*x4, x3*x4*x3*x4 ] [ x1*x3*x4*x3, x2, x2*x4*x3*x4, x3*x4*x3*x4 ] [ x2*x4*x3, x1*x2*x4*x3*x4, x2, x3*x4*x3*x4 ] [ x2*x3*x4*x3, x1*x2, x2*x4*x3*x4, x3*x4*x3*x4 ] [ x2*x4*x3, x1*x2*x4*x3*x4, x4*x3*x4, x3*x4*x3*x4 ] [ x1*x3*x4*x3, x1, x2, x3*x4*x3*x4 ] [ x1*x3*x4*x3, x1, x2*x4*x3*x4, x3*x4*x3*x4 ] [ x1*x3*x4*x3, x1, x4*x3*x4, x3*x4*x3*x4 ] [ x1*x3*x4*x3, x2, x2*x4*x3*x4, x3*x4*x3*x4 ] [ x1*x3*x4*x3, x1*x2*x4*x3*x4, x2, x3*x4*x3*x4 ] [ x1*x3*x4*x3, x1*x2, x2*x4*x3*x4, x3*x4*x3*x4 ] [ x1*x3*x4*x3, x1*x2*x4*x3*x4, x4*x3*x4, x3*x4*x3*x4 ] [ x1, x2, x2*x4*x3*x4, x3*x4*x3*x4 ] [ x1*x2*x4*x3, x1, x2, x3*x4*x3*x4 ] [ x1*x2*x3*x4*x3, x1, x2*x4*x3*x4, x3*x4*x3*x4 ] [ x1*x2*x4*x3, x1, x4*x3*x4, x3*x4*x3*x4 ] [ x3*x4*x3, x2, x2*x4*x3*x4, x3*x4*x3*x4 ] [ x1*x2*x4*x3, x1*x2*x4*x3*x4, x2, x3*x4*x3*x4 ] [ x1*x2*x3*x4*x3, x1*x2, x2*x4*x3*x4, x3*x4*x3*x4 ] [ x1*x2*x4*x3, x1*x2*x4*x3*x4, x4*x3*x4, x3*x4*x3*x4 ] [ x1*x3*x4*x3, x1, x2, x3*x4*x3*x4 ] [ x1*x3*x4*x3, x1, x1*x2*x4*x3*x4, x3*x4*x3*x4 ] [ x1*x3*x4*x3, x1, x1*x4*x3*x4, x3*x4*x3*x4 ] [ x1*x3*x4*x3, x2, x1*x2*x4*x3*x4, x3*x4*x3*x4 ] [ x1*x3*x4*x3, x2*x4*x3*x4, x2, x3*x4*x3*x4 ] [ x1*x3*x4*x3, x1*x2, x1*x2*x4*x3*x4, x3*x4*x3*x4 ] [ x1*x3*x4*x3, x2*x4*x3*x4, x1*x4*x3*x4, x3*x4*x3*x4 ] [ x1, x2, x1*x2*x4*x3*x4, x3*x4*x3*x4 ] [ x2*x4*x3, x1, x2, x3*x4*x3*x4 ] [ x1*x2*x3*x4*x3, x1, x1*x2*x4*x3*x4, x3*x4*x3*x4 ] [ x2*x4*x3, x1, x1*x4*x3*x4, x3*x4*x3*x4 ] [ x3*x4*x3, x2, x1*x2*x4*x3*x4, x3*x4*x3*x4 ] [ x2*x4*x3, x2*x4*x3*x4, x2, x3*x4*x3*x4 ] [ x1*x2*x3*x4*x3, x1*x2, x1*x2*x4*x3*x4, x3*x4*x3*x4 ] [ x2*x4*x3, x2*x4*x3*x4, x1*x4*x3*x4, x3*x4*x3*x4 ] [ x3*x4*x3, x1, x2, x3*x4*x3*x4 ] [ x3*x4*x3, x1, x1*x2*x4*x3*x4, x3*x4*x3*x4 ] [ x3*x4*x3, x1, x1*x4*x3*x4, x3*x4*x3*x4 ] [ x3*x4*x3, x2, x1*x2*x4*x3*x4, x3*x4*x3*x4 ] [ x3*x4*x3, x2*x4*x3*x4, x2, x3*x4*x3*x4 ] [ x3*x4*x3, x1*x2, x1*x2*x4*x3*x4, x3*x4*x3*x4 ] [ x3*x4*x3, x2*x4*x3*x4, x1*x4*x3*x4, x3*x4*x3*x4 ] [ x1, x2, x1*x2*x4*x3*x4, x3*x4*x3*x4 ] [ x1*x2*x4*x3, x1, x2, x3*x4*x3*x4 ] [ x2*x3*x4*x3, x1, x1*x2*x4*x3*x4, x3*x4*x3*x4 ] [ x1*x2*x4*x3, x1, x1*x4*x3*x4, x3*x4*x3*x4 ] [ x1*x3*x4*x3, x2, x1*x2*x4*x3*x4, x3*x4*x3*x4 ] [ x1*x2*x4*x3, x2*x4*x3*x4, x2, x3*x4*x3*x4 ] [ x2*x3*x4*x3, x1*x2, x1*x2*x4*x3*x4, x3*x4*x3*x4 ] [ x1*x2*x4*x3, x2*x4*x3*x4, x1*x4*x3*x4, x3*x4*x3*x4 ] [ x4, x1, x1*x2, x2*x4*x2*x4 ] [ x4, x1, x3, x2*x4*x2*x4 ] [ x4, x1, x1*x2*x3, x2*x4*x2*x4 ] [ x4, x1*x2, x3, x2*x4*x2*x4 ] [ x4, x1*x3, x1*x2, x2*x4*x2*x4 ] [ x4, x2, x3, x2*x4*x2*x4 ] [ x4, x1*x3, x1*x2*x3, x2*x4*x2*x4 ] [ x1, x1*x2, x3, x2*x4*x2*x4 ] [ x3*x4, x1, x1*x2, x2*x4*x2*x4 ] [ x1*x4*x2, x1, x3, x2*x4*x2*x4 ] [ x3*x4, x1, x1*x2*x3, x2*x4*x2*x4 ] [ x1*x4, x1*x2, x3, x2*x4*x2*x4 ] [ x3*x4, x1*x3, x1*x2, x2*x4*x2*x4 ] [ x1*x4*x2, x2, x3, x2*x4*x2*x4 ] [ x3*x4, x1*x3, x1*x2*x3, x2*x4*x2*x4 ] [ x4, x1, x2, x3*x4*x3*x4 ] [ x4, x1, x2*x3, x3*x4*x3*x4 ] [ x4, x1, x3, x3*x4*x3*x4 ] [ x4, x2, x2*x3, x3*x4*x3*x4 ] [ x4, x1*x2*x3, x2, x3*x4*x3*x4 ] [ x4, x1*x2, x2*x3, x3*x4*x3*x4 ] [ x4, x1*x2*x3, x3, x3*x4*x3*x4 ] [ x1, x2, x2*x3, x3*x4*x3*x4 ] [ x2*x4*x3, x1, x2, x3*x4*x3*x4 ] [ x2*x4, x1, x2*x3, x3*x4*x3*x4 ] [ x2*x4*x3, x1, x3, x3*x4*x3*x4 ] [ x1*x4, x2, x2*x3, x3*x4*x3*x4 ] [ x2*x4*x3, x1*x2*x3, x2, x3*x4*x3*x4 ] [ x2*x4, x1*x2, x2*x3, x3*x4*x3*x4 ] [ x2*x4*x3, x1*x2*x3, x3, x3*x4*x3*x4 ] [ x1*x4, x3, x1, x2*x3*x2*x3 ] [ x1*x4, x3, x2, x2*x3*x2*x3 ] [ x1*x4, x3, x1*x2, x2*x3*x2*x3 ] [ x1*x4, x1, x2, x2*x3*x2*x3 ] [ x1*x4, x3*x2, x1, x2*x3*x2*x3 ] [ x1*x4, x1*x3, x2, x2*x3*x2*x3 ] [ x1*x4, x3*x2, x1*x2, x2*x3*x2*x3 ] [ x3, x1, x2, x2*x3*x2*x3 ] [ x1*x2*x4, x3, x1, x2*x3*x2*x3 ] [ x4, x3, x2, x2*x3*x2*x3 ] [ x1*x2*x4, x3, x1*x2, x2*x3*x2*x3 ] [ x1*x3*x4, x1, x2, x2*x3*x2*x3 ] [ x1*x2*x4, x3*x2, x1, x2*x3*x2*x3 ] [ x4, x1*x3, x2, x2*x3*x2*x3 ] [ x1*x2*x4, x3*x2, x1*x2, x2*x3*x2*x3 ] [ x1*x4, x3, x1, x2*x3*x2*x3 ] [ x1*x4, x3, x2, x2*x3*x2*x3 ] [ x1*x4, x3, x1*x2, x2*x3*x2*x3 ] [ x1*x4, x1, x2, x2*x3*x2*x3 ] [ x1*x4, x3*x2, x1, x2*x3*x2*x3 ] [ x1*x4, x1*x3, x2, x2*x3*x2*x3 ] [ x1*x4, x3*x2, x1*x2, x2*x3*x2*x3 ] [ x3, x1, x2, x2*x3*x2*x3 ] [ x1*x2*x4, x3, x1, x2*x3*x2*x3 ] [ x4, x3, x2, x2*x3*x2*x3 ] [ x1*x2*x4, x3, x1*x2, x2*x3*x2*x3 ] [ x1*x3*x4, x1, x2, x2*x3*x2*x3 ] [ x1*x2*x4, x3*x2, x1, x2*x3*x2*x3 ] [ x4, x1*x3, x2, x2*x3*x2*x3 ] [ x1*x2*x4, x3*x2, x1*x2, x2*x3*x2*x3 ] [ x4, x3, x2, x1*x2*x1*x2 ] [ x4, x3, x2*x1*x2, x1*x2*x1*x2 ] [ x4, x3, x1*x2, x1*x2*x1*x2 ] [ x4, x2, x2*x1*x2, x1*x2*x1*x2 ] [ x4, x2*x1*x2*x3, x2, x1*x2*x1*x2 ] [ x4, x2*x3, x2*x1*x2, x1*x2*x1*x2 ] [ x4, x2*x1*x2*x3, x1*x2, x1*x2*x1*x2 ] [ x3, x2, x2*x1*x2, x1*x2*x1*x2 ] [ x2*x1*x2*x4, x3, x2, x1*x2*x1*x2 ] [ x2*x4, x3, x2*x1*x2, x1*x2*x1*x2 ] [ x2*x1*x2*x4, x3, x1*x2, x1*x2*x1*x2 ] [ x3*x4, x2, x2*x1*x2, x1*x2*x1*x2 ] [ x2*x1*x2*x4, x2*x1*x2*x3, x2, x1*x2*x1*x2 ] [ x2*x4, x2*x3, x2*x1*x2, x1*x2*x1*x2 ] [ x2*x1*x2*x4, x2*x1*x2*x3, x1*x2, x1*x2*x1*x2 ] [ x4, x3, x2, x1*x2*x1*x2 ] [ x4, x3, x2*x1*x2, x1*x2*x1*x2 ] [ x4, x3, x1*x2, x1*x2*x1*x2 ] [ x4, x2, x2*x1*x2, x1*x2*x1*x2 ] [ x4, x2*x1*x2*x3, x2, x1*x2*x1*x2 ] [ x4, x2*x3, x2*x1*x2, x1*x2*x1*x2 ] [ x4, x2*x1*x2*x3, x1*x2, x1*x2*x1*x2 ] [ x3, x2, x2*x1*x2, x1*x2*x1*x2 ] [ x2*x1*x2*x4, x3, x2, x1*x2*x1*x2 ] [ x2*x4, x3, x2*x1*x2, x1*x2*x1*x2 ] [ x2*x1*x2*x4, x3, x1*x2, x1*x2*x1*x2 ] [ x3*x4, x2, x2*x1*x2, x1*x2*x1*x2 ] [ x2*x1*x2*x4, x2*x1*x2*x3, x2, x1*x2*x1*x2 ] [ x2*x4, x2*x3, x2*x1*x2, x1*x2*x1*x2 ] [ x2*x1*x2*x4, x2*x1*x2*x3, x1*x2, x1*x2*x1*x2 ] [ x4, x4*x1*x4, x2, x1*x4*x1*x4 ] [ x4, x4*x1*x4, x3, x1*x4*x1*x4 ] [ x4, x4*x1*x4, x2*x3, x1*x4*x1*x4 ] [ x4, x2, x3, x1*x4*x1*x4 ] [ x4, x3*x4*x1*x4, x2, x1*x4*x1*x4 ] [ x4, x2*x4*x1*x4, x3, x1*x4*x1*x4 ] [ x4, x3*x4*x1*x4, x2*x3, x1*x4*x1*x4 ] [ x4*x1*x4, x2, x3, x1*x4*x1*x4 ] [ x3*x4, x4*x1*x4, x2, x1*x4*x1*x4 ] [ x2*x4, x4*x1*x4, x3, x1*x4*x1*x4 ] [ x3*x4, x4*x1*x4, x2*x3, x1*x4*x1*x4 ] [ x1*x4, x2, x3, x1*x4*x1*x4 ] [ x3*x4, x3*x4*x1*x4, x2, x1*x4*x1*x4 ] [ x2*x4, x2*x4*x1*x4, x3, x1*x4*x1*x4 ] [ x3*x4, x3*x4*x1*x4, x2*x3, x1*x4*x1*x4 ] [ x4, x1, x2, x3*x4*x3*x4 ] [ x4, x1, x3, x3*x4*x3*x4 ] [ x4, x1, x2*x3, x3*x4*x3*x4 ] [ x4, x2, x3, x3*x4*x3*x4 ] [ x4, x1*x3, x2, x3*x4*x3*x4 ] [ x4, x1*x2, x3, x3*x4*x3*x4 ] [ x4, x1*x3, x2*x3, x3*x4*x3*x4 ] [ x1, x2, x3, x3*x4*x3*x4 ] [ x4*x3, x1, x2, x3*x4*x3*x4 ] [ x2*x4, x1, x3, x3*x4*x3*x4 ] [ x4*x3, x1, x2*x3, x3*x4*x3*x4 ] [ x1*x4, x2, x3, x3*x4*x3*x4 ] [ x4*x3, x1*x3, x2, x3*x4*x3*x4 ] [ x2*x4, x1*x2, x3, x3*x4*x3*x4 ] [ x4*x3, x1*x3, x2*x3, x3*x4*x3*x4 ] [ x4, x1, x2, x3*x4*x3*x4 ] [ x4, x1, x3, x3*x4*x3*x4 ] [ x4, x1, x2*x3, x3*x4*x3*x4 ] [ x4, x2, x3, x3*x4*x3*x4 ] [ x4, x1*x3, x2, x3*x4*x3*x4 ] [ x4, x1*x2, x3, x3*x4*x3*x4 ] [ x4, x1*x3, x2*x3, x3*x4*x3*x4 ] [ x1, x2, x3, x3*x4*x3*x4 ] [ x4*x3, x1, x2, x3*x4*x3*x4 ] [ x2*x4, x1, x3, x3*x4*x3*x4 ] [ x4*x3, x1, x2*x3, x3*x4*x3*x4 ] [ x1*x4, x2, x3, x3*x4*x3*x4 ] [ x4*x3, x1*x3, x2, x3*x4*x3*x4 ] [ x2*x4, x1*x2, x3, x3*x4*x3*x4 ] [ x4*x3, x1*x3, x2*x3, x3*x4*x3*x4 ] [ x4, x1, x2, x4^2 ] [ x4, x1, x3, x4^2 ] [ x4, x1, x2*x3, x4^2 ] [ x4, x2, x3, x4^2 ] [ x4, x1*x3, x2, x4^2 ] [ x4, x1*x2, x3, x4^2 ] [ x4, x1*x3, x2*x3, x4^2 ] [ x1, x2, x3, x4^2 ] [ x3*x4, x1, x2, x4^2 ] [ x2*x4, x1, x3, x4^2 ] [ x3*x4, x1, x2*x3, x4^2 ] [ x4*x1, x2, x3, x4^2 ] [ x3*x4, x1*x3, x2, x4^2 ] [ x2*x4, x1*x2, x3, x4^2 ] [ x3*x4, x1*x3, x2*x3, x4^2 ] [ x4, x1, x2, x4^2 ] [ x4, x1, x3, x4^2 ] [ x4, x1, x2*x3, x4^2 ] [ x4, x2, x3, x4^2 ] [ x4, x1*x3, x2, x4^2 ] [ x4, x1*x2, x3, x4^2 ] [ x4, x1*x3, x2*x3, x4^2 ] [ x1, x2, x3, x4^2 ] [ x3*x4, x1, x2, x4^2 ] [ x4*x2, x1, x3, x4^2 ] [ x3*x4, x1, x2*x3, x4^2 ] [ x1*x4, x2, x3, x4^2 ] [ x3*x4, x1*x3, x2, x4^2 ] [ x4*x2, x1*x2, x3, x4^2 ] [ x3*x4, x1*x3, x2*x3, x4^2 ] [ x4, x1, x2, x3*x4*x3*x4 ] [ x4, x1, x1*x3, x3*x4*x3*x4 ] [ x4, x1, x1*x2*x3, x3*x4*x3*x4 ] [ x4, x2, x1*x3, x3*x4*x3*x4 ] [ x4, x3, x2, x3*x4*x3*x4 ] [ x4, x1*x2, x1*x3, x3*x4*x3*x4 ] [ x4, x3, x1*x2*x3, x3*x4*x3*x4 ] [ x1, x2, x1*x3, x3*x4*x3*x4 ] [ x1*x4*x3, x1, x2, x3*x4*x3*x4 ] [ x2*x4, x1, x1*x3, x3*x4*x3*x4 ] [ x1*x4*x3, x1, x1*x2*x3, x3*x4*x3*x4 ] [ x1*x4, x2, x1*x3, x3*x4*x3*x4 ] [ x1*x4*x3, x3, x2, x3*x4*x3*x4 ] [ x2*x4, x1*x2, x1*x3, x3*x4*x3*x4 ] [ x1*x4*x3, x3, x1*x2*x3, x3*x4*x3*x4 ] [ x4, x1, x2, x2*x4*x2*x4 ] [ x4, x1, x1*x3, x2*x4*x2*x4 ] [ x4, x1, x1*x2*x3, x2*x4*x2*x4 ] [ x4, x2, x1*x3, x2*x4*x2*x4 ] [ x4, x3, x2, x2*x4*x2*x4 ] [ x4, x1*x2, x1*x3, x2*x4*x2*x4 ] [ x4, x3, x1*x2*x3, x2*x4*x2*x4 ] [ x1, x2, x1*x3, x2*x4*x2*x4 ] [ x1*x3*x4, x1, x2, x2*x4*x2*x4 ] [ x4*x2, x1, x1*x3, x2*x4*x2*x4 ] [ x1*x3*x4, x1, x1*x2*x3, x2*x4*x2*x4 ] [ x1*x4, x2, x1*x3, x2*x4*x2*x4 ] [ x1*x3*x4, x3, x2, x2*x4*x2*x4 ] [ x4*x2, x1*x2, x1*x3, x2*x4*x2*x4 ] [ x1*x3*x4, x3, x1*x2*x3, x2*x4*x2*x4 ] [ x4, x1, x2, x3*x4*x3*x4 ] [ x4, x1, x1*x2*x3, x3*x4*x3*x4 ] [ x4, x1, x1*x3, x3*x4*x3*x4 ] [ x4, x2, x1*x2*x3, x3*x4*x3*x4 ] [ x4, x2*x3, x2, x3*x4*x3*x4 ] [ x4, x1*x2, x1*x2*x3, x3*x4*x3*x4 ] [ x4, x2*x3, x1*x3, x3*x4*x3*x4 ] [ x1, x2, x1*x2*x3, x3*x4*x3*x4 ] [ x1*x2*x4*x3, x1, x2, x3*x4*x3*x4 ] [ x2*x4, x1, x1*x2*x3, x3*x4*x3*x4 ] [ x1*x2*x4*x3, x1, x1*x3, x3*x4*x3*x4 ] [ x1*x4, x2, x1*x2*x3, x3*x4*x3*x4 ] [ x1*x2*x4*x3, x2*x3, x2, x3*x4*x3*x4 ] [ x2*x4, x1*x2, x1*x2*x3, x3*x4*x3*x4 ] [ x1*x2*x4*x3, x2*x3, x1*x3, x3*x4*x3*x4 ] [ x2*x4, x3, x1, x1*x3*x1*x3 ] [ x2*x4, x3, x2, x1*x3*x1*x3 ] [ x2*x4, x3, x1*x2, x1*x3*x1*x3 ] [ x2*x4, x1, x2, x1*x3*x1*x3 ] [ x2*x4, x2*x3, x1, x1*x3*x1*x3 ] [ x2*x4, x3*x1, x2, x1*x3*x1*x3 ] [ x2*x4, x2*x3, x1*x2, x1*x3*x1*x3 ] [ x3, x1, x2, x1*x3*x1*x3 ] [ x4, x3, x1, x1*x3*x1*x3 ] [ x1*x2*x4, x3, x2, x1*x3*x1*x3 ] [ x4, x3, x1*x2, x1*x3*x1*x3 ] [ x2*x3*x4, x1, x2, x1*x3*x1*x3 ] [ x4, x2*x3, x1, x1*x3*x1*x3 ] [ x1*x2*x4, x3*x1, x2, x1*x3*x1*x3 ] [ x4, x2*x3, x1*x2, x1*x3*x1*x3 ] [ x4, x1, x2, x3*x4*x3*x4 ] [ x4, x1, x3, x3*x4*x3*x4 ] [ x4, x1, x2*x3, x3*x4*x3*x4 ] [ x4, x2, x3, x3*x4*x3*x4 ] [ x4, x1*x3, x2, x3*x4*x3*x4 ] [ x4, x1*x2, x3, x3*x4*x3*x4 ] [ x4, x1*x3, x2*x3, x3*x4*x3*x4 ] [ x1, x2, x3, x3*x4*x3*x4 ] [ x4*x3, x1, x2, x3*x4*x3*x4 ] [ x2*x4, x1, x3, x3*x4*x3*x4 ] [ x4*x3, x1, x2*x3, x3*x4*x3*x4 ] [ x1*x4, x2, x3, x3*x4*x3*x4 ] [ x4*x3, x1*x3, x2, x3*x4*x3*x4 ] [ x2*x4, x1*x2, x3, x3*x4*x3*x4 ] [ x4*x3, x1*x3, x2*x3, x3*x4*x3*x4 ] [ x4, x1, x2, x4^2 ] [ x4, x1, x3, x4^2 ] [ x4, x1, x2*x3, x4^2 ] [ x4, x2, x3, x4^2 ] [ x4, x1*x3, x2, x4^2 ] [ x4, x1*x2, x3, x4^2 ] [ x4, x1*x3, x2*x3, x4^2 ] [ x1, x2, x3, x4^2 ] [ x3*x4, x1, x2, x4^2 ] [ x2*x4, x1, x3, x4^2 ] [ x3*x4, x1, x2*x3, x4^2 ] [ x4*x1, x2, x3, x4^2 ] [ x3*x4, x1*x3, x2, x4^2 ] [ x2*x4, x1*x2, x3, x4^2 ] [ x3*x4, x1*x3, x2*x3, x4^2 ] [ x4, x2*x3*x2, x1, x2*x3*x2*x3 ] [ x4, x2*x3*x2, x1*x3*x2*x3, x2*x3*x2*x3 ] [ x4, x2*x3*x2, x3*x2*x3, x2*x3*x2*x3 ] [ x4, x1, x1*x3*x2*x3, x2*x3*x2*x3 ] [ x4, x1*x3*x2, x1, x2*x3*x2*x3 ] [ x4, x1*x2*x3*x2, x1*x3*x2*x3, x2*x3*x2*x3 ] [ x4, x1*x3*x2, x3*x2*x3, x2*x3*x2*x3 ] [ x2*x3*x2, x1, x1*x3*x2*x3, x2*x3*x2*x3 ] [ x1*x3*x2*x3*x4, x2*x3*x2, x1, x2*x3*x2*x3 ] [ x1*x4, x2*x3*x2, x1*x3*x2*x3, x2*x3*x2*x3 ] [ x1*x3*x2*x3*x4, x2*x3*x2, x3*x2*x3, x2*x3*x2*x3 ] [ x2*x3*x2*x4, x1, x1*x3*x2*x3, x2*x3*x2*x3 ] [ x1*x3*x2*x3*x4, x1*x3*x2, x1, x2*x3*x2*x3 ] [ x1*x4, x1*x2*x3*x2, x1*x3*x2*x3, x2*x3*x2*x3 ] [ x1*x3*x2*x3*x4, x1*x3*x2, x3*x2*x3, x2*x3*x2*x3 ] [ x4, x2*x3*x2, x1, x2*x3*x2*x3 ] [ x4, x2*x3*x2, x1*x3*x2*x3, x2*x3*x2*x3 ] [ x4, x2*x3*x2, x3*x2*x3, x2*x3*x2*x3 ] [ x4, x1, x1*x3*x2*x3, x2*x3*x2*x3 ] [ x4, x1*x3*x2, x1, x2*x3*x2*x3 ] [ x4, x1*x2*x3*x2, x1*x3*x2*x3, x2*x3*x2*x3 ] [ x4, x1*x3*x2, x3*x2*x3, x2*x3*x2*x3 ] [ x2*x3*x2, x1, x1*x3*x2*x3, x2*x3*x2*x3 ] [ x1*x3*x2*x3*x4, x2*x3*x2, x1, x2*x3*x2*x3 ] [ x1*x4, x2*x3*x2, x1*x3*x2*x3, x2*x3*x2*x3 ] [ x1*x3*x2*x3*x4, x2*x3*x2, x3*x2*x3, x2*x3*x2*x3 ] [ x2*x3*x2*x4, x1, x1*x3*x2*x3, x2*x3*x2*x3 ] [ x1*x3*x2*x3*x4, x1*x3*x2, x1, x2*x3*x2*x3 ] [ x1*x4, x1*x2*x3*x2, x1*x3*x2*x3, x2*x3*x2*x3 ] [ x1*x3*x2*x3*x4, x1*x3*x2, x3*x2*x3, x2*x3*x2*x3 ] [ x4, x3, x1, x2*x3*x2*x3 ] [ x4, x3, x2, x2*x3*x2*x3 ] [ x4, x3, x1*x2, x2*x3*x2*x3 ] [ x4, x1, x2, x2*x3*x2*x3 ] [ x4, x3*x2, x1, x2*x3*x2*x3 ] [ x4, x1*x3, x2, x2*x3*x2*x3 ] [ x4, x3*x2, x1*x2, x2*x3*x2*x3 ] [ x3, x1, x2, x2*x3*x2*x3 ] [ x2*x4, x3, x1, x2*x3*x2*x3 ] [ x1*x4, x3, x2, x2*x3*x2*x3 ] [ x2*x4, x3, x1*x2, x2*x3*x2*x3 ] [ x3*x4, x1, x2, x2*x3*x2*x3 ] [ x2*x4, x3*x2, x1, x2*x3*x2*x3 ] [ x1*x4, x1*x3, x2, x2*x3*x2*x3 ] [ x2*x4, x3*x2, x1*x2, x2*x3*x2*x3 ] [ x1*x4, x3, x1, x3^2 ] [ x1*x4, x3, x2, x3^2 ] [ x1*x4, x3, x1*x2, x3^2 ] [ x1*x4, x1, x2, x3^2 ] [ x1*x4, x3*x2, x1, x3^2 ] [ x1*x4, x1*x3, x2, x3^2 ] [ x1*x4, x3*x2, x1*x2, x3^2 ] [ x3, x1, x2, x3^2 ] [ x1*x2*x4, x3, x1, x3^2 ] [ x4, x3, x2, x3^2 ] [ x1*x2*x4, x3, x1*x2, x3^2 ] [ x1*x3*x4, x1, x2, x3^2 ] [ x1*x2*x4, x3*x2, x1, x3^2 ] [ x4, x1*x3, x2, x3^2 ] [ x1*x2*x4, x3*x2, x1*x2, x3^2 ] [ x4*x5, x4, x3, x2, x3^2 ] [ x4*x5, x4, x3, x1, x3^2 ] [ x4*x5, x4, x3, x1*x2, x3^2 ] [ x4*x5, x4, x2, x1, x3^2 ] [ x4*x5, x4, x1*x3, x2, x3^2 ] [ x4*x5, x4, x2*x3, x1, x3^2 ] [ x4*x5, x4, x1*x3, x1*x2, x3^2 ] [ x4*x5, x3, x2, x1, x3^2 ] [ x4*x5, x1*x4, x3, x2, x3^2 ] [ x4*x5, x2*x4, x3, x1, x3^2 ] [ x4*x5, x1*x4, x3, x1*x2, x3^2 ] [ x4*x5, x3*x4, x2, x1, x3^2 ] [ x4*x5, x1*x4, x1*x3, x2, x3^2 ] [ x4*x5, x2*x4, x2*x3, x1, x3^2 ] [ x4*x5, x1*x4, x1*x3, x1*x2, x3^2 ] [ x4, x3, x2, x1, x3^2 ] [ x1*x4*x5, x4, x3, x2, x3^2 ] [ x2*x4*x5, x4, x3, x1, x3^2 ] [ x1*x4*x5, x4, x3, x1*x2, x3^2 ] [ x3*x4*x5, x4, x2, x1, x3^2 ] [ x1*x4*x5, x4, x1*x3, x2, x3^2 ] [ x2*x4*x5, x4, x2*x3, x1, x3^2 ] [ x1*x4*x5, x4, x1*x3, x1*x2, x3^2 ] [ x5, x3, x2, x1, x3^2 ] [ x1*x4*x5, x1*x4, x3, x2, x3^2 ] [ x2*x4*x5, x2*x4, x3, x1, x3^2 ] [ x1*x4*x5, x1*x4, x3, x1*x2, x3^2 ] [ x3*x4*x5, x3*x4, x2, x1, x3^2 ] [ x1*x4*x5, x1*x4, x1*x3, x2, x3^2 ] [ x2*x4*x5, x2*x4, x2*x3, x1, x3^2 ] [ x1*x4*x5, x1*x4, x1*x3, x1*x2, x3^2 ] [ x1*x5, x3*x4*x3, x1, x2, x3*x4*x3*x4 ] [ x1*x5, x3*x4*x3, x1, x2*x4*x3*x4, x3*x4*x3*x4 ] [ x1*x5, x3*x4*x3, x1, x4*x3*x4, x3*x4*x3*x4 ] [ x1*x5, x3*x4*x3, x2, x2*x4*x3*x4, x3*x4*x3*x4 ] [ x1*x5, x3*x4*x3, x1*x2*x4*x3*x4, x2, x3*x4*x3*x4 ] [ x1*x5, x3*x4*x3, x1*x2, x2*x4*x3*x4, x3*x4*x3*x4 ] [ x1*x5, x3*x4*x3, x1*x2*x4*x3*x4, x4*x3*x4, x3*x4*x3*x4 ] [ x1*x5, x1, x2, x2*x4*x3*x4, x3*x4*x3*x4 ] [ x1*x5, x2*x4*x3, x1, x2, x3*x4*x3*x4 ] [ x1*x5, x2*x3*x4*x3, x1, x2*x4*x3*x4, x3*x4*x3*x4 ] [ x1*x5, x2*x4*x3, x1, x4*x3*x4, x3*x4*x3*x4 ] [ x1*x5, x1*x3*x4*x3, x2, x2*x4*x3*x4, x3*x4*x3*x4 ] [ x1*x5, x2*x4*x3, x1*x2*x4*x3*x4, x2, x3*x4*x3*x4 ] [ x1*x5, x2*x3*x4*x3, x1*x2, x2*x4*x3*x4, x3*x4*x3*x4 ] [ x1*x5, x2*x4*x3, x1*x2*x4*x3*x4, x4*x3*x4, x3*x4*x3*x4 ] [ x3*x4*x3, x1, x2, x2*x4*x3*x4, x3*x4*x3*x4 ] [ x1*x2*x4*x3*x4*x5, x3*x4*x3, x1, x2, x3*x4*x3*x4 ] [ x1*x2*x5, x3*x4*x3, x1, x2*x4*x3*x4, x3*x4*x3*x4 ] [ x1*x2*x4*x3*x4*x5, x3*x4*x3, x1, x4*x3*x4, x3*x4*x3*x4 ] [ x5, x3*x4*x3, x2, x2*x4*x3*x4, x3*x4*x3*x4 ] [ x1*x2*x4*x3*x4*x5, x3*x4*x3, x1*x2*x4*x3*x4, x2, x3*x4*x3*x4 ] [ x1*x2*x5, x3*x4*x3, x1*x2, x2*x4*x3*x4, x3*x4*x3*x4 ] [ x1*x2*x4*x3*x4*x5, x3*x4*x3, x1*x2*x4*x3*x4, x4*x3*x4, x3*x4*x3*x4 ] [ x1*x3*x4*x3*x5, x1, x2, x2*x4*x3*x4, x3*x4*x3*x4 ] [ x1*x2*x4*x3*x4*x5, x2*x4*x3, x1, x2, x3*x4*x3*x4 ] [ x1*x2*x5, x2*x3*x4*x3, x1, x2*x4*x3*x4, x3*x4*x3*x4 ] [ x1*x2*x4*x3*x4*x5, x2*x4*x3, x1, x4*x3*x4, x3*x4*x3*x4 ] [ x5, x1*x3*x4*x3, x2, x2*x4*x3*x4, x3*x4*x3*x4 ] [ x1*x2*x4*x3*x4*x5, x2*x4*x3, x1*x2*x4*x3*x4, x2, x3*x4*x3*x4 ] [ x1*x2*x5, x2*x3*x4*x3, x1*x2, x2*x4*x3*x4, x3*x4*x3*x4 ] [ x1*x2*x4*x3*x4*x5, x2*x4*x3, x1*x2*x4*x3*x4, x4*x3*x4, x3*x4*x3*x4 ] [ x5, x5*x1*x5, x2, x3, x1*x5*x1*x5 ] [ x5, x5*x1*x5, x2, x2*x3*x4, x1*x5*x1*x5 ] [ x5, x5*x1*x5, x2, x2*x4, x1*x5*x1*x5 ] [ x5, x5*x1*x5, x3, x2*x3*x4, x1*x5*x1*x5 ] [ x5, x5*x1*x5, x3*x4, x3, x1*x5*x1*x5 ] [ x5, x5*x1*x5, x2*x3, x2*x3*x4, x1*x5*x1*x5 ] [ x5, x5*x1*x5, x3*x4, x2*x4, x1*x5*x1*x5 ] [ x5, x2, x3, x2*x3*x4, x1*x5*x1*x5 ] [ x5, x2*x3*x4*x5*x1*x5, x2, x3, x1*x5*x1*x5 ] [ x5, x3*x5*x1*x5, x2, x2*x3*x4, x1*x5*x1*x5 ] [ x5, x2*x3*x4*x5*x1*x5, x2, x2*x4, x1*x5*x1*x5 ] [ x5, x2*x5*x1*x5, x3, x2*x3*x4, x1*x5*x1*x5 ] [ x5, x2*x3*x4*x5*x1*x5, x3*x4, x3, x1*x5*x1*x5 ] [ x5, x3*x5*x1*x5, x2*x3, x2*x3*x4, x1*x5*x1*x5 ] [ x5, x2*x3*x4*x5*x1*x5, x3*x4, x2*x4, x1*x5*x1*x5 ] [ x5*x1*x5, x2, x3, x2*x3*x4, x1*x5*x1*x5 ] [ x2*x3*x4*x5, x5*x1*x5, x2, x3, x1*x5*x1*x5 ] [ x3*x5, x5*x1*x5, x2, x2*x3*x4, x1*x5*x1*x5 ] [ x2*x3*x4*x5, x5*x1*x5, x2, x2*x4, x1*x5*x1*x5 ] [ x2*x5, x5*x1*x5, x3, x2*x3*x4, x1*x5*x1*x5 ] [ x2*x3*x4*x5, x5*x1*x5, x3*x4, x3, x1*x5*x1*x5 ] [ x3*x5, x5*x1*x5, x2*x3, x2*x3*x4, x1*x5*x1*x5 ] [ x2*x3*x4*x5, x5*x1*x5, x3*x4, x2*x4, x1*x5*x1*x5 ] [ x1*x5, x2, x3, x2*x3*x4, x1*x5*x1*x5 ] [ x2*x3*x4*x5, x2*x3*x4*x5*x1*x5, x2, x3, x1*x5*x1*x5 ] [ x3*x5, x3*x5*x1*x5, x2, x2*x3*x4, x1*x5*x1*x5 ] [ x2*x3*x4*x5, x2*x3*x4*x5*x1*x5, x2, x2*x4, x1*x5*x1*x5 ] [ x2*x5, x2*x5*x1*x5, x3, x2*x3*x4, x1*x5*x1*x5 ] [ x2*x3*x4*x5, x2*x3*x4*x5*x1*x5, x3*x4, x3, x1*x5*x1*x5 ] [ x3*x5, x3*x5*x1*x5, x2*x3, x2*x3*x4, x1*x5*x1*x5 ] [ x2*x3*x4*x5, x2*x3*x4*x5*x1*x5, x3*x4, x2*x4, x1*x5*x1*x5 ] [ x5, x4, x4*x1*x4, x2, x1*x4*x1*x4 ] [ x5, x4, x4*x1*x4, x3, x1*x4*x1*x4 ] [ x5, x4, x4*x1*x4, x2*x3, x1*x4*x1*x4 ] [ x5, x4, x2, x3, x1*x4*x1*x4 ] [ x5, x4, x3*x4*x1*x4, x2, x1*x4*x1*x4 ] [ x5, x4, x2*x4*x1*x4, x3, x1*x4*x1*x4 ] [ x5, x4, x3*x4*x1*x4, x2*x3, x1*x4*x1*x4 ] [ x5, x4*x1*x4, x2, x3, x1*x4*x1*x4 ] [ x5, x3*x4, x4*x1*x4, x2, x1*x4*x1*x4 ] [ x5, x2*x4, x4*x1*x4, x3, x1*x4*x1*x4 ] [ x5, x3*x4, x4*x1*x4, x2*x3, x1*x4*x1*x4 ] [ x5, x1*x4, x2, x3, x1*x4*x1*x4 ] [ x5, x3*x4, x3*x4*x1*x4, x2, x1*x4*x1*x4 ] [ x5, x2*x4, x2*x4*x1*x4, x3, x1*x4*x1*x4 ] [ x5, x3*x4, x3*x4*x1*x4, x2*x3, x1*x4*x1*x4 ] [ x4, x4*x1*x4, x2, x3, x1*x4*x1*x4 ] [ x3*x5, x4, x4*x1*x4, x2, x1*x4*x1*x4 ] [ x2*x5, x4, x4*x1*x4, x3, x1*x4*x1*x4 ] [ x3*x5, x4, x4*x1*x4, x2*x3, x1*x4*x1*x4 ] [ x4*x1*x4*x5, x4, x2, x3, x1*x4*x1*x4 ] [ x3*x5, x4, x3*x4*x1*x4, x2, x1*x4*x1*x4 ] [ x2*x5, x4, x2*x4*x1*x4, x3, x1*x4*x1*x4 ] [ x3*x5, x4, x3*x4*x1*x4, x2*x3, x1*x4*x1*x4 ] [ x4*x5, x4*x1*x4, x2, x3, x1*x4*x1*x4 ] [ x3*x5, x3*x4, x4*x1*x4, x2, x1*x4*x1*x4 ] [ x2*x5, x2*x4, x4*x1*x4, x3, x1*x4*x1*x4 ] [ x3*x5, x3*x4, x4*x1*x4, x2*x3, x1*x4*x1*x4 ] [ x4*x1*x4*x5, x1*x4, x2, x3, x1*x4*x1*x4 ] [ x3*x5, x3*x4, x3*x4*x1*x4, x2, x1*x4*x1*x4 ] [ x2*x5, x2*x4, x2*x4*x1*x4, x3, x1*x4*x1*x4 ] [ x3*x5, x3*x4, x3*x4*x1*x4, x2*x3, x1*x4*x1*x4 ] [ x5, x1, x2, x3, x2*x5*x2*x5 ] [ x5, x1, x2, x1*x3*x4, x2*x5*x2*x5 ] [ x5, x1, x2, x1*x4, x2*x5*x2*x5 ] [ x5, x1, x3, x1*x3*x4, x2*x5*x2*x5 ] [ x5, x1, x1*x2*x3*x4, x3, x2*x5*x2*x5 ] [ x5, x1, x2*x3, x1*x3*x4, x2*x5*x2*x5 ] [ x5, x1, x1*x2*x3*x4, x1*x4, x2*x5*x2*x5 ] [ x5, x2, x3, x1*x3*x4, x2*x5*x2*x5 ] [ x5, x3*x4, x2, x3, x2*x5*x2*x5 ] [ x5, x1*x3, x2, x1*x3*x4, x2*x5*x2*x5 ] [ x5, x3*x4, x2, x1*x4, x2*x5*x2*x5 ] [ x5, x1*x2, x3, x1*x3*x4, x2*x5*x2*x5 ] [ x5, x3*x4, x1*x2*x3*x4, x3, x2*x5*x2*x5 ] [ x5, x1*x3, x2*x3, x1*x3*x4, x2*x5*x2*x5 ] [ x5, x3*x4, x1*x2*x3*x4, x1*x4, x2*x5*x2*x5 ] [ x1, x2, x3, x1*x3*x4, x2*x5*x2*x5 ] [ x1*x3*x4*x5, x1, x2, x3, x2*x5*x2*x5 ] [ x3*x5, x1, x2, x1*x3*x4, x2*x5*x2*x5 ] [ x1*x3*x4*x5, x1, x2, x1*x4, x2*x5*x2*x5 ] [ x5*x2, x1, x3, x1*x3*x4, x2*x5*x2*x5 ] [ x1*x3*x4*x5, x1, x1*x2*x3*x4, x3, x2*x5*x2*x5 ] [ x3*x5, x1, x2*x3, x1*x3*x4, x2*x5*x2*x5 ] [ x1*x3*x4*x5, x1, x1*x2*x3*x4, x1*x4, x2*x5*x2*x5 ] [ x1*x5, x2, x3, x1*x3*x4, x2*x5*x2*x5 ] [ x1*x3*x4*x5, x3*x4, x2, x3, x2*x5*x2*x5 ] [ x3*x5, x1*x3, x2, x1*x3*x4, x2*x5*x2*x5 ] [ x1*x3*x4*x5, x3*x4, x2, x1*x4, x2*x5*x2*x5 ] [ x5*x2, x1*x2, x3, x1*x3*x4, x2*x5*x2*x5 ] [ x1*x3*x4*x5, x3*x4, x1*x2*x3*x4, x3, x2*x5*x2*x5 ] [ x3*x5, x1*x3, x2*x3, x1*x3*x4, x2*x5*x2*x5 ] [ x1*x3*x4*x5, x3*x4, x1*x2*x3*x4, x1*x4, x2*x5*x2*x5 ] [ x5, x4, x1, x2, x4^2 ] [ x5, x4, x1, x3, x4^2 ] [ x5, x4, x1, x2*x3, x4^2 ] [ x5, x4, x2, x3, x4^2 ] [ x5, x4, x1*x3, x2, x4^2 ] [ x5, x4, x1*x2, x3, x4^2 ] [ x5, x4, x1*x3, x2*x3, x4^2 ] [ x5, x1, x2, x3, x4^2 ] [ x5, x3*x4, x1, x2, x4^2 ] [ x5, x2*x4, x1, x3, x4^2 ] [ x5, x3*x4, x1, x2*x3, x4^2 ] [ x5, x4*x1, x2, x3, x4^2 ] [ x5, x3*x4, x1*x3, x2, x4^2 ] [ x5, x2*x4, x1*x2, x3, x4^2 ] [ x5, x3*x4, x1*x3, x2*x3, x4^2 ] [ x4, x1, x2, x3, x4^2 ] [ x3*x5, x4, x1, x2, x4^2 ] [ x2*x5, x4, x1, x3, x4^2 ] [ x3*x5, x4, x1, x2*x3, x4^2 ] [ x1*x5, x4, x2, x3, x4^2 ] [ x3*x5, x4, x1*x3, x2, x4^2 ] [ x2*x5, x4, x1*x2, x3, x4^2 ] [ x3*x5, x4, x1*x3, x2*x3, x4^2 ] [ x4*x5, x1, x2, x3, x4^2 ] [ x3*x5, x3*x4, x1, x2, x4^2 ] [ x2*x5, x2*x4, x1, x3, x4^2 ] [ x3*x5, x3*x4, x1, x2*x3, x4^2 ] [ x1*x5, x4*x1, x2, x3, x4^2 ] [ x3*x5, x3*x4, x1*x3, x2, x4^2 ] [ x2*x5, x2*x4, x1*x2, x3, x4^2 ] [ x3*x5, x3*x4, x1*x3, x2*x3, x4^2 ] [ x5, x1, x2, x3, x3*x5*x3*x5 ] [ x5, x1, x2, x4, x3*x5*x3*x5 ] [ x5, x1, x2, x3*x4, x3*x5*x3*x5 ] [ x5, x1, x3, x4, x3*x5*x3*x5 ] [ x5, x1, x2*x4, x3, x3*x5*x3*x5 ] [ x5, x1, x2*x3, x4, x3*x5*x3*x5 ] [ x5, x1, x2*x4, x3*x4, x3*x5*x3*x5 ] [ x5, x2, x3, x4, x3*x5*x3*x5 ] [ x5, x1*x4, x2, x3, x3*x5*x3*x5 ] [ x5, x1*x3, x2, x4, x3*x5*x3*x5 ] [ x5, x1*x4, x2, x3*x4, x3*x5*x3*x5 ] [ x5, x1*x2, x3, x4, x3*x5*x3*x5 ] [ x5, x1*x4, x2*x4, x3, x3*x5*x3*x5 ] [ x5, x1*x3, x2*x3, x4, x3*x5*x3*x5 ] [ x5, x1*x4, x2*x4, x3*x4, x3*x5*x3*x5 ] [ x1, x2, x3, x4, x3*x5*x3*x5 ] [ x4*x5, x1, x2, x3, x3*x5*x3*x5 ] [ x5*x3, x1, x2, x4, x3*x5*x3*x5 ] [ x4*x5, x1, x2, x3*x4, x3*x5*x3*x5 ] [ x2*x5, x1, x3, x4, x3*x5*x3*x5 ] [ x4*x5, x1, x2*x4, x3, x3*x5*x3*x5 ] [ x5*x3, x1, x2*x3, x4, x3*x5*x3*x5 ] [ x4*x5, x1, x2*x4, x3*x4, x3*x5*x3*x5 ] [ x1*x5, x2, x3, x4, x3*x5*x3*x5 ] [ x4*x5, x1*x4, x2, x3, x3*x5*x3*x5 ] [ x5*x3, x1*x3, x2, x4, x3*x5*x3*x5 ] [ x4*x5, x1*x4, x2, x3*x4, x3*x5*x3*x5 ] [ x2*x5, x1*x2, x3, x4, x3*x5*x3*x5 ] [ x4*x5, x1*x4, x2*x4, x3, x3*x5*x3*x5 ] [ x5*x3, x1*x3, x2*x3, x4, x3*x5*x3*x5 ] [ x4*x5, x1*x4, x2*x4, x3*x4, x3*x5*x3*x5 ] [ x2*x5, x4, x1, x2, x3*x4*x3*x4 ] [ x2*x5, x4, x1, x1*x3, x3*x4*x3*x4 ] [ x2*x5, x4, x1, x1*x2*x3, x3*x4*x3*x4 ] [ x2*x5, x4, x2, x1*x3, x3*x4*x3*x4 ] [ x2*x5, x4, x3, x2, x3*x4*x3*x4 ] [ x2*x5, x4, x1*x2, x1*x3, x3*x4*x3*x4 ] [ x2*x5, x4, x3, x1*x2*x3, x3*x4*x3*x4 ] [ x2*x5, x1, x2, x1*x3, x3*x4*x3*x4 ] [ x2*x5, x1*x4*x3, x1, x2, x3*x4*x3*x4 ] [ x2*x5, x2*x4, x1, x1*x3, x3*x4*x3*x4 ] [ x2*x5, x1*x4*x3, x1, x1*x2*x3, x3*x4*x3*x4 ] [ x2*x5, x1*x4, x2, x1*x3, x3*x4*x3*x4 ] [ x2*x5, x1*x4*x3, x3, x2, x3*x4*x3*x4 ] [ x2*x5, x2*x4, x1*x2, x1*x3, x3*x4*x3*x4 ] [ x2*x5, x1*x4*x3, x3, x1*x2*x3, x3*x4*x3*x4 ] [ x4, x1, x2, x1*x3, x3*x4*x3*x4 ] [ x1*x2*x3*x5, x4, x1, x2, x3*x4*x3*x4 ] [ x5, x4, x1, x1*x3, x3*x4*x3*x4 ] [ x1*x2*x3*x5, x4, x1, x1*x2*x3, x3*x4*x3*x4 ] [ x1*x2*x5, x4, x2, x1*x3, x3*x4*x3*x4 ] [ x1*x2*x3*x5, x4, x3, x2, x3*x4*x3*x4 ] [ x5, x4, x1*x2, x1*x3, x3*x4*x3*x4 ] [ x1*x2*x3*x5, x4, x3, x1*x2*x3, x3*x4*x3*x4 ] [ x2*x4*x5, x1, x2, x1*x3, x3*x4*x3*x4 ] [ x1*x2*x3*x5, x1*x4*x3, x1, x2, x3*x4*x3*x4 ] [ x5, x2*x4, x1, x1*x3, x3*x4*x3*x4 ] [ x1*x2*x3*x5, x1*x4*x3, x1, x1*x2*x3, x3*x4*x3*x4 ] [ x1*x2*x5, x1*x4, x2, x1*x3, x3*x4*x3*x4 ] [ x1*x2*x3*x5, x1*x4*x3, x3, x2, x3*x4*x3*x4 ] [ x5, x2*x4, x1*x2, x1*x3, x3*x4*x3*x4 ] [ x1*x2*x3*x5, x1*x4*x3, x3, x1*x2*x3, x3*x4*x3*x4 ] [ x5, x5*x1*x5, x2, x3, x1*x5*x1*x5 ] [ x5, x5*x1*x5, x2, x4, x1*x5*x1*x5 ] [ x5, x5*x1*x5, x2, x3*x4, x1*x5*x1*x5 ] [ x5, x5*x1*x5, x3, x4, x1*x5*x1*x5 ] [ x5, x5*x1*x5, x2*x4, x3, x1*x5*x1*x5 ] [ x5, x5*x1*x5, x2*x3, x4, x1*x5*x1*x5 ] [ x5, x5*x1*x5, x2*x4, x3*x4, x1*x5*x1*x5 ] [ x5, x2, x3, x4, x1*x5*x1*x5 ] [ x5, x4*x5*x1*x5, x2, x3, x1*x5*x1*x5 ] [ x5, x3*x5*x1*x5, x2, x4, x1*x5*x1*x5 ] [ x5, x4*x5*x1*x5, x2, x3*x4, x1*x5*x1*x5 ] [ x5, x2*x5*x1*x5, x3, x4, x1*x5*x1*x5 ] [ x5, x4*x5*x1*x5, x2*x4, x3, x1*x5*x1*x5 ] [ x5, x3*x5*x1*x5, x2*x3, x4, x1*x5*x1*x5 ] [ x5, x4*x5*x1*x5, x2*x4, x3*x4, x1*x5*x1*x5 ] [ x5*x1*x5, x2, x3, x4, x1*x5*x1*x5 ] [ x4*x5, x5*x1*x5, x2, x3, x1*x5*x1*x5 ] [ x3*x5, x5*x1*x5, x2, x4, x1*x5*x1*x5 ] [ x4*x5, x5*x1*x5, x2, x3*x4, x1*x5*x1*x5 ] [ x2*x5, x5*x1*x5, x3, x4, x1*x5*x1*x5 ] [ x4*x5, x5*x1*x5, x2*x4, x3, x1*x5*x1*x5 ] [ x3*x5, x5*x1*x5, x2*x3, x4, x1*x5*x1*x5 ] [ x4*x5, x5*x1*x5, x2*x4, x3*x4, x1*x5*x1*x5 ] [ x1*x5, x2, x3, x4, x1*x5*x1*x5 ] [ x4*x5, x4*x5*x1*x5, x2, x3, x1*x5*x1*x5 ] [ x3*x5, x3*x5*x1*x5, x2, x4, x1*x5*x1*x5 ] [ x4*x5, x4*x5*x1*x5, x2, x3*x4, x1*x5*x1*x5 ] [ x2*x5, x2*x5*x1*x5, x3, x4, x1*x5*x1*x5 ] [ x4*x5, x4*x5*x1*x5, x2*x4, x3, x1*x5*x1*x5 ] [ x3*x5, x3*x5*x1*x5, x2*x3, x4, x1*x5*x1*x5 ] [ x4*x5, x4*x5*x1*x5, x2*x4, x3*x4, x1*x5*x1*x5 ] [ x5, x5*x1*x5, x2, x3, x1*x5*x1*x5 ] [ x5, x5*x1*x5, x2, x4, x1*x5*x1*x5 ] [ x5, x5*x1*x5, x2, x3*x4, x1*x5*x1*x5 ] [ x5, x5*x1*x5, x3, x4, x1*x5*x1*x5 ] [ x5, x5*x1*x5, x2*x4, x3, x1*x5*x1*x5 ] [ x5, x5*x1*x5, x2*x3, x4, x1*x5*x1*x5 ] [ x5, x5*x1*x5, x2*x4, x3*x4, x1*x5*x1*x5 ] [ x5, x2, x3, x4, x1*x5*x1*x5 ] [ x5, x4*x5*x1*x5, x2, x3, x1*x5*x1*x5 ] [ x5, x3*x5*x1*x5, x2, x4, x1*x5*x1*x5 ] [ x5, x4*x5*x1*x5, x2, x3*x4, x1*x5*x1*x5 ] [ x5, x2*x5*x1*x5, x3, x4, x1*x5*x1*x5 ] [ x5, x4*x5*x1*x5, x2*x4, x3, x1*x5*x1*x5 ] [ x5, x3*x5*x1*x5, x2*x3, x4, x1*x5*x1*x5 ] [ x5, x4*x5*x1*x5, x2*x4, x3*x4, x1*x5*x1*x5 ] [ x5*x1*x5, x2, x3, x4, x1*x5*x1*x5 ] [ x4*x5, x5*x1*x5, x2, x3, x1*x5*x1*x5 ] [ x3*x5, x5*x1*x5, x2, x4, x1*x5*x1*x5 ] [ x4*x5, x5*x1*x5, x2, x3*x4, x1*x5*x1*x5 ] [ x2*x5, x5*x1*x5, x3, x4, x1*x5*x1*x5 ] [ x4*x5, x5*x1*x5, x2*x4, x3, x1*x5*x1*x5 ] [ x3*x5, x5*x1*x5, x2*x3, x4, x1*x5*x1*x5 ] [ x4*x5, x5*x1*x5, x2*x4, x3*x4, x1*x5*x1*x5 ] [ x1*x5, x2, x3, x4, x1*x5*x1*x5 ] [ x4*x5, x4*x5*x1*x5, x2, x3, x1*x5*x1*x5 ] [ x3*x5, x3*x5*x1*x5, x2, x4, x1*x5*x1*x5 ] [ x4*x5, x4*x5*x1*x5, x2, x3*x4, x1*x5*x1*x5 ] [ x2*x5, x2*x5*x1*x5, x3, x4, x1*x5*x1*x5 ] [ x4*x5, x4*x5*x1*x5, x2*x4, x3, x1*x5*x1*x5 ] [ x3*x5, x3*x5*x1*x5, x2*x3, x4, x1*x5*x1*x5 ] [ x4*x5, x4*x5*x1*x5, x2*x4, x3*x4, x1*x5*x1*x5 ] [ x5, x1, x2, x3, x4*x5*x4*x5 ] [ x5, x1, x2, x4, x4*x5*x4*x5 ] [ x5, x1, x2, x3*x4, x4*x5*x4*x5 ] [ x5, x1, x3, x4, x4*x5*x4*x5 ] [ x5, x1, x2*x4, x3, x4*x5*x4*x5 ] [ x5, x1, x2*x3, x4, x4*x5*x4*x5 ] [ x5, x1, x2*x4, x3*x4, x4*x5*x4*x5 ] [ x5, x2, x3, x4, x4*x5*x4*x5 ] [ x5, x1*x4, x2, x3, x4*x5*x4*x5 ] [ x5, x1*x3, x2, x4, x4*x5*x4*x5 ] [ x5, x1*x4, x2, x3*x4, x4*x5*x4*x5 ] [ x5, x1*x2, x3, x4, x4*x5*x4*x5 ] [ x5, x1*x4, x2*x4, x3, x4*x5*x4*x5 ] [ x5, x1*x3, x2*x3, x4, x4*x5*x4*x5 ] [ x5, x1*x4, x2*x4, x3*x4, x4*x5*x4*x5 ] [ x1, x2, x3, x4, x4*x5*x4*x5 ] [ x5*x4, x1, x2, x3, x4*x5*x4*x5 ] [ x3*x5, x1, x2, x4, x4*x5*x4*x5 ] [ x5*x4, x1, x2, x3*x4, x4*x5*x4*x5 ] [ x2*x5, x1, x3, x4, x4*x5*x4*x5 ] [ x5*x4, x1, x2*x4, x3, x4*x5*x4*x5 ] [ x3*x5, x1, x2*x3, x4, x4*x5*x4*x5 ] [ x5*x4, x1, x2*x4, x3*x4, x4*x5*x4*x5 ] [ x1*x5, x2, x3, x4, x4*x5*x4*x5 ] [ x5*x4, x1*x4, x2, x3, x4*x5*x4*x5 ] [ x3*x5, x1*x3, x2, x4, x4*x5*x4*x5 ] [ x5*x4, x1*x4, x2, x3*x4, x4*x5*x4*x5 ] [ x2*x5, x1*x2, x3, x4, x4*x5*x4*x5 ] [ x5*x4, x1*x4, x2*x4, x3, x4*x5*x4*x5 ] [ x3*x5, x1*x3, x2*x3, x4, x4*x5*x4*x5 ] [ x5*x4, x1*x4, x2*x4, x3*x4, x4*x5*x4*x5 ] [ x5, x1, x2, x3, x4*x5*x4*x5 ] [ x5, x1, x2, x4, x4*x5*x4*x5 ] [ x5, x1, x2, x3*x4, x4*x5*x4*x5 ] [ x5, x1, x3, x4, x4*x5*x4*x5 ] [ x5, x1, x2*x4, x3, x4*x5*x4*x5 ] [ x5, x1, x2*x3, x4, x4*x5*x4*x5 ] [ x5, x1, x2*x4, x3*x4, x4*x5*x4*x5 ] [ x5, x2, x3, x4, x4*x5*x4*x5 ] [ x5, x1*x4, x2, x3, x4*x5*x4*x5 ] [ x5, x1*x3, x2, x4, x4*x5*x4*x5 ] [ x5, x1*x4, x2, x3*x4, x4*x5*x4*x5 ] [ x5, x1*x2, x3, x4, x4*x5*x4*x5 ] [ x5, x1*x4, x2*x4, x3, x4*x5*x4*x5 ] [ x5, x1*x3, x2*x3, x4, x4*x5*x4*x5 ] [ x5, x1*x4, x2*x4, x3*x4, x4*x5*x4*x5 ] [ x1, x2, x3, x4, x4*x5*x4*x5 ] [ x5*x4, x1, x2, x3, x4*x5*x4*x5 ] [ x3*x5, x1, x2, x4, x4*x5*x4*x5 ] [ x5*x4, x1, x2, x3*x4, x4*x5*x4*x5 ] [ x2*x5, x1, x3, x4, x4*x5*x4*x5 ] [ x5*x4, x1, x2*x4, x3, x4*x5*x4*x5 ] [ x3*x5, x1, x2*x3, x4, x4*x5*x4*x5 ] [ x5*x4, x1, x2*x4, x3*x4, x4*x5*x4*x5 ] [ x1*x5, x2, x3, x4, x4*x5*x4*x5 ] [ x5*x4, x1*x4, x2, x3, x4*x5*x4*x5 ] [ x3*x5, x1*x3, x2, x4, x4*x5*x4*x5 ] [ x5*x4, x1*x4, x2, x3*x4, x4*x5*x4*x5 ] [ x2*x5, x1*x2, x3, x4, x4*x5*x4*x5 ] [ x5*x4, x1*x4, x2*x4, x3, x4*x5*x4*x5 ] [ x3*x5, x1*x3, x2*x3, x4, x4*x5*x4*x5 ] [ x5*x4, x1*x4, x2*x4, x3*x4, x4*x5*x4*x5 ] [ x1*x2, x2^2 ] [ x1, x2^2 ] [ x2, x2^2 ] [ x2, x1*x2*x1*x2 ] [ x1, x1*x2*x1*x2 ] [ x2*x1, x1*x2*x1*x2 ] gap> LogTo();