gap> RequirePackage("carat"); true gap> names := []; [ ] gap> GROUPS := []; [ ] gap> R := CaratReadBravaisFile("ordnung.128/(2)^6(4)^2(8)^1/group.1258"); 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, 0, -1, 0, 0 ], [ 0, 0, -1, 0, 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, 0, -1, 0, 0 ], [ 0, 0, -1, 0, 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)^6(4)^2(8)^1/words.group.1258"]); gap> Append(GROUPS,[P1]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^1(4)^2(8)^2/group.1259"); 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, 0, 1, 0, 0 ], [ 0, 0, -1, 0, 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> P2 := Group(R.generators); gap> Append(names,["ordnung.16/(2)^1(4)^2(8)^2/words.group.1259"]); gap> Append(GROUPS,[P2]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^1(4)^6(8)^2/group.1260"); 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, 0, 1, 0, 0 ], [ 0, 0, -1, 0, 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)^6(8)^2/words.group.1260"]); gap> Append(GROUPS,[P3]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^1(4)^6(8)^2/group.1261"); rec( generators := [ [ [ 0, -1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, -1, 0, 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)^1(4)^6(8)^2/words.group.1261"]); gap> Append(GROUPS,[P4]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^1(4)^6(8)^2/group.1262"); 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, 0, 1, 0, 0 ], [ 0, 0, -1, 0, 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> P5 := Group(R.generators); gap> Append(names,["ordnung.16/(2)^1(4)^6(8)^2/words.group.1262"]); gap> Append(GROUPS,[P5]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^1(4)^6(8)^2/group.1263"); rec( generators := [ [ [ 0, -1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, -1, 0, 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> P6 := Group(R.generators); gap> Append(names,["ordnung.16/(2)^1(4)^6(8)^2/words.group.1263"]); gap> Append(GROUPS,[P6]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^1(4)^6(8)^2/min.250"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, -1, 0, 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, 0, -1, 0, 0 ], [ 0, 0, -1, 0, 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)^1(4)^6(8)^2/words.min.250"]); gap> Append(GROUPS,[P7]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^1(4)^6(8)^2/min.251"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, -1, 0, 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, 0, -1, 0, 0 ], [ 0, 0, -1, 0, 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)^1(4)^6(8)^2/words.min.251"]); gap> Append(GROUPS,[P8]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^1(4)^6(8)^2/min.252"); 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, 0, -1, 0, 0 ], [ 0, 0, 1, 0, 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)^1(4)^6(8)^2/words.min.252"]); gap> Append(GROUPS,[P9]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^2(4)^2(8)^1/group.1264"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, -1, 0, 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, 0, -1, 0, 0 ], [ 0, 0, 1, 0, 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(4)^2(8)^1/words.group.1264"]); gap> Append(GROUPS,[P10]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^2(4)^2(8)^1/group.1265"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, -1, 0, 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, 0, -1, 0, 0 ], [ 0, 0, 1, 0, 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)^2(4)^2(8)^1/words.group.1265"]); gap> Append(GROUPS,[P11]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^2(4)^2(8)^1/group.1266"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 1, 0, 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> P12 := Group(R.generators); gap> Append(names,["ordnung.16/(2)^2(4)^2(8)^1/words.group.1266"]); gap> Append(GROUPS,[P12]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^4(8)^3/group.1267"); 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, 0, -1, 0, 0 ], [ 0, 0, -1, 0, 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(8)^3/words.group.1267"]); gap> Append(GROUPS,[P13]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^4(8)^3/group.1268"); 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, 0, -1, 0, 0 ], [ 0, 0, -1, 0, 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(8)^3/words.group.1268"]); gap> Append(GROUPS,[P14]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^4(8)^3/group.1269"); rec( generators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, -1, 0, 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(8)^3/words.group.1269"]); gap> Append(GROUPS,[P15]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^4(8)^3/group.1270"); rec( generators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, -1, 0, 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(8)^3/words.group.1270"]); gap> Append(GROUPS,[P16]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^4(8)^3/min.253"); 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 ] ], [ [ 0, -1, 0, 0, 0, 0 ], [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 1, 0, 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(8)^3/words.min.253"]); gap> Append(GROUPS,[P17]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^4(8)^3/min.254"); 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 ] ], [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 1, 0, 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)^3/words.min.254"]); gap> Append(GROUPS,[P18]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^4(8)^3/min.255"); 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 ] ], [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 1, 0, 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)^3/words.min.255"]); gap> Append(GROUPS,[P19]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^1(4)^6(8)^2/group.1271"); 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, 0, 1, 0, 0 ], [ 0, 0, -1, 0, 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> P20 := Group(R.generators); gap> Append(names,["ordnung.32/(2)^1(4)^6(8)^2/words.group.1271"]); gap> Append(GROUPS,[P20]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^1(4)^6(8)^2/group.1272"); 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, 0, 1, 0, 0 ], [ 0, 0, -1, 0, 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> P21 := Group(R.generators); gap> Append(names,["ordnung.32/(2)^1(4)^6(8)^2/words.group.1272"]); gap> Append(GROUPS,[P21]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^2(4)^2(8)^1/group.1273"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, -1, 0, 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, 0, -1, 0, 0 ], [ 0, 0, 1, 0, 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> P22 := Group(R.generators); gap> Append(names,["ordnung.32/(2)^2(4)^2(8)^1/words.group.1273"]); gap> Append(GROUPS,[P22]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^2(8)^1/group.1274"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 1, 0, 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, 0, 1, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 32 ) gap> P23 := Group(R.generators); gap> Append(names,["ordnung.32/(2)^4(4)^2(8)^1/words.group.1274"]); gap> Append(GROUPS,[P23]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^2(8)^1/group.1275"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, -1, 0, 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, 0, 1, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 32 ) gap> P24 := Group(R.generators); gap> Append(names,["ordnung.32/(2)^4(4)^2(8)^1/words.group.1275"]); gap> Append(GROUPS,[P24]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^2(8)^1/group.1276"); 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 ] ] , [ [ 0, 1, 0, 0, 0, 0 ], [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 32 ) gap> P25 := Group(R.generators); gap> Append(names,["ordnung.32/(2)^4(4)^2(8)^1/words.group.1276"]); gap> Append(GROUPS,[P25]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^2(8)^1/group.1277"); 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 ] ], [ [ 0, 1, 0, 0, 0, 0 ], [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 32 ) gap> P26 := Group(R.generators); gap> Append(names,["ordnung.32/(2)^4(4)^2(8)^1/words.group.1277"]); gap> Append(GROUPS,[P26]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^2(8)^1/group.1278"); 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 ] ], [ [ 0, 1, 0, 0, 0, 0 ], [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] ], size := 32 ) gap> P27 := Group(R.generators); gap> Append(names,["ordnung.32/(2)^4(4)^2(8)^1/words.group.1278"]); gap> Append(GROUPS,[P27]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^2(8)^1/group.1279"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 1, 0, 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, 0, 1, 0, 0 ], [ 0, 0, -1, 0, 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)^4(4)^2(8)^1/words.group.1279"]); gap> Append(GROUPS,[P28]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^4(8)^1/group.1280"); 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, 0, -1, 0, 0 ], [ 0, 0, -1, 0, 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)^4(4)^4(8)^1/words.group.1280"]); gap> Append(GROUPS,[P29]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^4(8)^1/group.1281"); 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, 0, -1, 0, 0 ], [ 0, 0, -1, 0, 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)^4(4)^4(8)^1/words.group.1281"]); gap> Append(GROUPS,[P30]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^4(8)^1/group.1282"); rec( generators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, -1, 0, 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> P31 := Group(R.generators); gap> Append(names,["ordnung.32/(2)^4(4)^4(8)^1/words.group.1282"]); gap> Append(GROUPS,[P31]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^4(8)^1/group.1283"); rec( generators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, -1, 0, 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> P32 := Group(R.generators); gap> Append(names,["ordnung.32/(2)^4(4)^4(8)^1/words.group.1283"]); gap> Append(GROUPS,[P32]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^4(8)^1/group.1284"); rec( generators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, -1, 0, 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> P33 := Group(R.generators); gap> Append(names,["ordnung.32/(2)^4(4)^4(8)^1/words.group.1284"]); gap> Append(GROUPS,[P33]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^4(8)^1/group.1285"); rec( generators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, -1, 0, 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> P34 := Group(R.generators); gap> Append(names,["ordnung.32/(2)^4(4)^4(8)^1/words.group.1285"]); gap> Append(GROUPS,[P34]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^4(8)^1/group.1286"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, -1, 0, 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, 0, -1, 0, 0 ], [ 0, 0, 1, 0, 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)^4(8)^1/words.group.1286"]); gap> Append(GROUPS,[P35]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^4(8)^1/group.1287"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, -1, 0, 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, 0, -1, 0, 0 ], [ 0, 0, 1, 0, 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)^4(8)^1/words.group.1287"]); gap> Append(GROUPS,[P36]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^4(8)^1/group.1288"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, -1, 0, 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> P37 := Group(R.generators); gap> Append(names,["ordnung.32/(2)^4(4)^4(8)^1/words.group.1288"]); gap> Append(GROUPS,[P37]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^4(8)^1/group.1289"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, -1, 0, 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, 0, -1, 0, 0 ], [ 0, 0, -1, 0, 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)^4(8)^1/words.group.1289"]); gap> Append(GROUPS,[P38]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^4(8)^1/group.1290"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, -1, 0, 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, 0, -1, 0, 0 ], [ 0, 0, -1, 0, 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)^4(8)^1/words.group.1290"]); gap> Append(GROUPS,[P39]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^4(8)^1/group.1291"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 1, 0, 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)^4(8)^1/words.group.1291"]); gap> Append(GROUPS,[P40]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^4(8)^1/group.1292"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, -1, 0, 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, 0, -1, 0, 0 ], [ 0, 0, -1, 0, 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)^4(8)^1/words.group.1292"]); gap> Append(GROUPS,[P41]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^4(8)^1/group.1293"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, -1, 0, 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, 0, -1, 0, 0 ], [ 0, 0, -1, 0, 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)^4(8)^1/words.group.1293"]); gap> Append(GROUPS,[P42]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^4(8)^1/group.1294"); 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 ] ], [ [ 0, -1, 0, 0, 0, 0 ], [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, -1, 0, 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)^4(8)^1/words.group.1294"]); gap> Append(GROUPS,[P43]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^4(8)^1/group.1295"); 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 ] ] , [ [ 0, -1, 0, 0, 0, 0 ], [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, -1, 0, 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)^4(8)^1/words.group.1295"]); gap> Append(GROUPS,[P44]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(8)^3/group.1296"); 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, 0, -1, 0, 0 ], [ 0, 0, -1, 0, 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> P45 := Group(R.generators); gap> Append(names,["ordnung.32/(2)^4(8)^3/words.group.1296"]); gap> Append(GROUPS,[P45]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(8)^3/group.1297"); 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 ] ], [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, -1, 0, 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(8)^3/words.group.1297"]); gap> Append(GROUPS,[P46]); gap> R := CaratReadBravaisFile("ordnung.64/(2)^4(4)^2(8)^1/group.1298"); 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 ] ], [ [ 0, 1, 0, 0, 0, 0 ], [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, -1, 0, 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> P47 := Group(R.generators); gap> Append(names,["ordnung.64/(2)^4(4)^2(8)^1/words.group.1298"]); gap> Append(GROUPS,[P47]); gap> R := CaratReadBravaisFile("ordnung.64/(2)^4(4)^4(8)^1/group.1299"); 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, 0, -1, 0, 0 ], [ 0, 0, -1, 0, 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> P48 := Group(R.generators); gap> Append(names,["ordnung.64/(2)^4(4)^4(8)^1/words.group.1299"]); gap> Append(GROUPS,[P48]); gap> R := CaratReadBravaisFile("ordnung.64/(2)^4(4)^4(8)^1/group.1300"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, -1, 0, 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> P49 := Group(R.generators); gap> Append(names,["ordnung.64/(2)^4(4)^4(8)^1/words.group.1300"]); gap> Append(GROUPS,[P49]); gap> R := CaratReadBravaisFile("ordnung.64/(2)^4(4)^4(8)^1/group.1301"); rec( generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, -1, 0, 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, 0, -1, 0, 0 ], [ 0, 0, -1, 0, 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> P50 := Group(R.generators); gap> Append(names,["ordnung.64/(2)^4(4)^4(8)^1/words.group.1301"]); gap> Append(GROUPS,[P50]); gap> R := CaratReadBravaisFile("ordnung.64/(2)^6(4)^2(8)^1/group.1302"); 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, 0, -1, 0, 0 ], [ 0, 0, -1, 0, 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, 0, -1, 0, 0 ], [ 0, 0, -1, 0, 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> P51 := Group(R.generators); gap> Append(names,["ordnung.64/(2)^6(4)^2(8)^1/words.group.1302"]); gap> Append(GROUPS,[P51]); gap> R := CaratReadBravaisFile("ordnung.64/(2)^6(4)^2(8)^1/group.1303"); 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, 0, -1, 0, 0 ], [ 0, 0, -1, 0, 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, 0, -1, 0, 0 ], [ 0, 0, -1, 0, 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> P52 := Group(R.generators); gap> Append(names,["ordnung.64/(2)^6(4)^2(8)^1/words.group.1303"]); gap> Append(GROUPS,[P52]); gap> R := CaratReadBravaisFile("ordnung.64/(2)^6(4)^2(8)^1/group.1304"); 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, 0, -1, 0, 0 ], [ 0, 0, -1, 0, 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, 0, -1, 0, 0 ], [ 0, 0, -1, 0, 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> P53 := Group(R.generators); gap> Append(names,["ordnung.64/(2)^6(4)^2(8)^1/words.group.1304"]); gap> Append(GROUPS,[P53]); gap> R := CaratReadBravaisFile("ordnung.64/(2)^6(4)^2(8)^1/group.1305"); 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, 0, -1, 0, 0 ], [ 0, 0, -1, 0, 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, 0, -1, 0, 0 ], [ 0, 0, -1, 0, 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> P54 := Group(R.generators); gap> Append(names,["ordnung.64/(2)^6(4)^2(8)^1/words.group.1305"]); gap> Append(GROUPS,[P54]); gap> R := CaratReadBravaisFile("ordnung.64/(2)^6(4)^2(8)^1/group.1306"); 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, 0, -1, 0, 0 ], [ 0, 0, -1, 0, 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, 0, -1, 0, 0 ], [ 0, 0, -1, 0, 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> P55 := Group(R.generators); gap> Append(names,["ordnung.64/(2)^6(4)^2(8)^1/words.group.1306"]); gap> Append(GROUPS,[P55]); gap> R := CaratReadBravaisFile("ordnung.64/(2)^6(4)^2(8)^1/group.1307"); 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, 0, -1, 0, 0 ], [ 0, 0, -1, 0, 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, 0, -1, 0, 0 ], [ 0, 0, -1, 0, 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> P56 := Group(R.generators); gap> Append(names,["ordnung.64/(2)^6(4)^2(8)^1/words.group.1307"]); gap> Append(GROUPS,[P56]); gap> R := CaratReadBravaisFile("ordnung.8/(2)^1(4)^2(8)^2/min.256"); 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, 0, -1, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 8 ) gap> P57 := Group(R.generators); gap> Append(names,["ordnung.8/(2)^1(4)^2(8)^2/words.min.256"]); gap> Append(GROUPS,[P57]); gap> R := CaratReadBravaisFile("ordnung.8/(2)^1(4)^2(8)^2/min.257"); 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, 0, 1, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] ], size := 8 ) gap> P58 := Group(R.generators); gap> Append(names,["ordnung.8/(2)^1(4)^2(8)^2/words.min.257"]); gap> Append(GROUPS,[P58]); gap> R := CaratReadBravaisFile("ordnung.8/(2)^1(4)^2(8)^2/min.258"); 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, 0, -1, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ], size := 8 ) gap> P59 := Group(R.generators); gap> Append(names,["ordnung.8/(2)^1(4)^2(8)^2/words.min.258"]); gap> Append(GROUPS,[P59]); gap> Print(GROUPS,"\n"); [ 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, 0, -1, 0, 0 ], [ 0, 0, -1, 0, 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, 0, -1, 0, 0 ], [ 0, 0, -1, 0, 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 ] ], [ [ 0, -1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, -1, 0, 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 ] ], [ [ 0, -1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, -1, 0, 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, 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0, 0, -1, 0, 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, 0, -1, 0, 0 ], [ 0, 0, -1, 0, 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 ] ], [ [ 0, -1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 1, 0, 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, 0, 1, 0, 0 ], [ 0, 0, -1, 0, 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, 0, -1, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ] ]) ] gap> Print(names,"\n"); [ "ordnung.128/(2)^6(4)^2(8)^1/words.group.1258", "ordnung.16/(2)^1(4)^2(8)^2/words.group.1259", "ordnung.16/(2)^1(4)^6(8)^2/words.group.1260", "ordnung.16/(2)^1(4)^6(8)^2/words.group.1261", "ordnung.16/(2)^1(4)^6(8)^2/words.group.1262", "ordnung.16/(2)^1(4)^6(8)^2/words.group.1263", "ordnung.16/(2)^1(4)^6(8)^2/words.min.250", "ordnung.16/(2)^1(4)^6(8)^2/words.min.251", "ordnung.16/(2)^1(4)^6(8)^2/words.min.252", "ordnung.16/(2)^2(4)^2(8)^1/words.group.1264", "ordnung.16/(2)^2(4)^2(8)^1/words.group.1265", "ordnung.16/(2)^2(4)^2(8)^1/words.group.1266", "ordnung.16/(2)^4(8)^3/words.group.1267", "ordnung.16/(2)^4(8)^3/words.group.1268", "ordnung.16/(2)^4(8)^3/words.group.1269", "ordnung.16/(2)^4(8)^3/words.group.1270", "ordnung.16/(2)^4(8)^3/words.min.253", "ordnung.16/(2)^4(8)^3/words.min.254" , "ordnung.16/(2)^4(8)^3/words.min.255", "ordnung.32/(2)^1(4)^6(8)^2/words.group.1271", "ordnung.32/(2)^1(4)^6(8)^2/words.group.1272", "ordnung.32/(2)^2(4)^2(8)^1/words.group.1273", "ordnung.32/(2)^4(4)^2(8)^1/words.group.1274", "ordnung.32/(2)^4(4)^2(8)^1/words.group.1275", "ordnung.32/(2)^4(4)^2(8)^1/words.group.1276", "ordnung.32/(2)^4(4)^2(8)^1/words.group.1277", "ordnung.32/(2)^4(4)^2(8)^1/words.group.1278", "ordnung.32/(2)^4(4)^2(8)^1/words.group.1279", "ordnung.32/(2)^4(4)^4(8)^1/words.group.1280", "ordnung.32/(2)^4(4)^4(8)^1/words.group.1281", "ordnung.32/(2)^4(4)^4(8)^1/words.group.1282", "ordnung.32/(2)^4(4)^4(8)^1/words.group.1283", "ordnung.32/(2)^4(4)^4(8)^1/words.group.1284", "ordnung.32/(2)^4(4)^4(8)^1/words.group.1285", "ordnung.32/(2)^4(4)^4(8)^1/words.group.1286", "ordnung.32/(2)^4(4)^4(8)^1/words.group.1287", "ordnung.32/(2)^4(4)^4(8)^1/words.group.1288", "ordnung.32/(2)^4(4)^4(8)^1/words.group.1289", "ordnung.32/(2)^4(4)^4(8)^1/words.group.1290", "ordnung.32/(2)^4(4)^4(8)^1/words.group.1291", "ordnung.32/(2)^4(4)^4(8)^1/words.group.1292", "ordnung.32/(2)^4(4)^4(8)^1/words.group.1293", "ordnung.32/(2)^4(4)^4(8)^1/words.group.1294", "ordnung.32/(2)^4(4)^4(8)^1/words.group.1295", "ordnung.32/(2)^4(8)^3/words.group.1296", "ordnung.32/(2)^4(8)^3/words.group.1297", "ordnung.64/(2)^4(4)^2(8)^1/words.group.1298", "ordnung.64/(2)^4(4)^4(8)^1/words.group.1299", "ordnung.64/(2)^4(4)^4(8)^1/words.group.1300", "ordnung.64/(2)^4(4)^4(8)^1/words.group.1301", "ordnung.64/(2)^6(4)^2(8)^1/words.group.1302", "ordnung.64/(2)^6(4)^2(8)^1/words.group.1303", "ordnung.64/(2)^6(4)^2(8)^1/words.group.1304", "ordnung.64/(2)^6(4)^2(8)^1/words.group.1305", "ordnung.64/(2)^6(4)^2(8)^1/words.group.1306", "ordnung.64/(2)^6(4)^2(8)^1/words.group.1307", "ordnung.8/(2)^1(4)^2(8)^2/words.min.256", "ordnung.8/(2)^1(4)^2(8)^2/words.min.257", "ordnung.8/(2)^1(4)^2(8)^2/words.min.258" ] gap> Size(GROUPS); 59 gap> Size(names); 59 gap> Read("../../TGROUPS.GAP"); gap> for i in [1..Size(GROUPS)] do > SubgroupWords(GROUPS[i], names[i]); > od; [ x5, x2*x1*x2*x3*x4*x3, x1, x2, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x5, x2*x1*x2*x3*x4*x3, x1, x1*x2*x1*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x5, x2*x1*x2*x3*x4*x3, x1, x1*x2*x1*x2*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x5, x2*x1*x2*x3*x4*x3, x2, x1*x2*x1*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x5, x2*x1*x2*x3*x4*x3, x2*x1*x4*x3*x4, x2, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x5, x2*x1*x2*x3*x4*x3, x1*x2, x1*x2*x1*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x5, x2*x1*x2*x3*x4*x3, x2*x1*x4*x3*x4, x1*x2*x1*x2*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x5, x1, x2, x1*x2*x1*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x5, x2*x1*x4*x3, x1, x2, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x5, x1*x2*x3*x4*x3, x1, x1*x2*x1*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x5, x2*x1*x4*x3, x1, x1*x2*x1*x2*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x5, x1*x2*x1*x2*x3*x4*x3, x2, x1*x2*x1*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x5, x2*x1*x4*x3, x2*x1*x4*x3*x4, x2, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x5, x1*x2*x3*x4*x3, x1*x2, x1*x2*x1*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x5, x2*x1*x4*x3, x2*x1*x4*x3*x4, x1*x2*x1*x2*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x1*x2*x3*x4*x3, x1, x2, x1*x2*x1*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x1*x2*x1*x4*x3*x4*x5, x2*x1*x2*x3*x4*x3, x1, x2, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x5, x2*x1*x2*x3*x4*x3, x1, x1*x2*x1*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x1*x2*x1*x4*x3*x4*x5, x2*x1*x2*x3*x4*x3, x1, x1*x2*x1*x2*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x1*x5, x2*x1*x2*x3*x4*x3, x2, x1*x2*x1*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x1*x2*x1*x4*x3*x4*x5, x2*x1*x2*x3*x4*x3, x2*x1*x4*x3*x4, x2, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x5, x2*x1*x2*x3*x4*x3, x1*x2, x1*x2*x1*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x1*x2*x1*x4*x3*x4*x5, x2*x1*x2*x3*x4*x3, x2*x1*x4*x3*x4, x1*x2*x1*x2*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x1*x2*x3*x4*x3*x5, x1, x2, x1*x2*x1*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x1*x2*x1*x4*x3*x4*x5, x2*x1*x4*x3, x1, x2, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x5, x1*x2*x3*x4*x3, x1, x1*x2*x1*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x1*x2*x1*x4*x3*x4*x5, x2*x1*x4*x3, x1, x1*x2*x1*x2*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x1*x5, x1*x2*x1*x2*x3*x4*x3, x2, x1*x2*x1*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x1*x2*x1*x4*x3*x4*x5, x2*x1*x4*x3, x2*x1*x4*x3*x4, x2, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x5, x1*x2*x3*x4*x3, x1*x2, x1*x2*x1*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x1*x2*x1*x4*x3*x4*x5, x2*x1*x4*x3, x2*x1*x4*x3*x4, x1*x2*x1*x2*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x3, x2, x2^2 ] [ x3, x1, x2^2 ] [ x3, x1*x2, x2^2 ] [ x2, x1, x2^2 ] [ x1*x3, x2, x2^2 ] [ x2*x3, x1, x2^2 ] [ x1*x3, x1*x2, x2^2 ] [ x3, x1, x2^2 ] [ x3, x2, x2^2 ] [ x3, x1*x2, x2^2 ] [ x1, x2, x2^2 ] [ x2^3*x3, x1, x2^2 ] [ x1*x3, x2, x2^2 ] [ x2^3*x3, x1*x2, x2^2 ] [ 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 ] [ x2^2*x3, x1, x2^2 ] [ x2^2*x3, x2, x2^2 ] [ x2^2*x3, x1*x2, x2^2 ] [ x1, x2, x2^2 ] [ x2*x3, x1, x2^2 ] [ x1*x2^2*x3, x2, x2^2 ] [ x2*x3, x1*x2, x2^2 ] [ 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 ] [ x2, x1^2, x1^3*x2*x1*x2 ] [ x1, x1^2, x1^3*x2*x1*x2 ] [ x2*x1, x1^2, x1^3*x2*x1*x2 ] [ x2, x1^2, x1^3*x2*x1*x2 ] [ x1, x1^2, x1^3*x2*x1*x2 ] [ x2*x1, x1^2, x1^3*x2*x1*x2 ] [ x2, x2^2, x1*x2*x1*x2^3 ] [ x1, x2^2, x1*x2*x1*x2^3 ] [ x2*x1, x2^2, x1*x2*x1*x2^3 ] [ x1*x2, x1^2*x2^2, x1^2 ] [ x1, x1^2*x2^2, x1^2 ] [ x1^2*x2, x1^2*x2^2, x1^2 ] [ x1*x2, x1^2*x2^2, x1^2 ] [ x1, x1^2*x2^2, x1^2 ] [ x1^2*x2, x1^2*x2^2, x1^2 ] [ x2, x2^2, x1^2 ] [ x1, x2^2, x1^2 ] [ x1*x2, x2^2, x1^2 ] [ x2, x2^2, x1*x2*x1*x2^3 ] [ x1, x2^2, x1*x2*x1*x2^3 ] [ x2*x1, x2^2, x1*x2*x1*x2^3 ] [ x2, x2^2, x1*x2*x1*x2^3 ] [ x1, x2^2, x1*x2*x1*x2^3 ] [ x2*x1, x2^2, x1*x2*x1*x2^3 ] [ x2, x1^2, x1^3*x2*x1*x2 ] [ x1, x1^2, x1^3*x2*x1*x2 ] [ x2*x1, x1^2, x1^3*x2*x1*x2 ] [ x2, x1^2, x1^3*x2*x1*x2 ] [ x1, x1^2, x1^3*x2*x1*x2 ] [ x2*x1, x1^2, x1^3*x2*x1*x2 ] [ x1*x2, x2^2, x1^2 ] [ x1, x2^2, x1^2 ] [ x2, x2^2, x1^2 ] [ x1*x2, x2^2, x1^2 ] [ x1, x2^2, x1^2 ] [ x2, x2^2, x1^2 ] [ x1^3*x2, x2^2, x1^2 ] [ x1, x2^2, x1^2 ] [ x1^2*x2, x2^2, x1^2 ] [ x4, x3, x1, x2^2 ] [ x4, x3, x2, x2^2 ] [ x4, x3, x1*x2, x2^2 ] [ x4, x1, x2, x2^2 ] [ x4, x2^3*x3, x1, x2^2 ] [ x4, x1*x3, x2, x2^2 ] [ x4, x2^3*x3, x1*x2, x2^2 ] [ x3, x1, x2, x2^2 ] [ x2*x4, x3, x1, x2^2 ] [ x1*x4, x3, x2, x2^2 ] [ x2*x4, x3, x1*x2, x2^2 ] [ x3*x4, x1, x2, x2^2 ] [ x2*x4, x2^3*x3, x1, x2^2 ] [ x1*x4, x1*x3, x2, x2^2 ] [ x2*x4, x2^3*x3, x1*x2, x2^2 ] [ x3, x2, x2^2, x1*x2*x1*x2^3 ] [ x3, x1, x2^2, x1*x2*x1*x2^3 ] [ x3, x2*x1, x2^2, x1*x2*x1*x2^3 ] [ x2, x1, x2^2, x1*x2*x1*x2^3 ] [ x1*x3, x2, x2^2, x1*x2*x1*x2^3 ] [ x2*x3, x1, x2^2, x1*x2*x1*x2^3 ] [ x1*x3, x2*x1, x2^2, x1*x2*x1*x2^3 ] [ x3, x1*x2, x1^2*x2^2, x1^2 ] [ x3, x1, x1^2*x2^2, x1^2 ] [ x3, x1^2*x2, x1^2*x2^2, x1^2 ] [ x1*x2, x1, x1^2*x2^2, x1^2 ] [ x1*x3, x1*x2, x1^2*x2^2, x1^2 ] [ x1*x2*x3, x1, x1^2*x2^2, x1^2 ] [ x1*x3, x1^2*x2, x1^2*x2^2, x1^2 ] [ x3, x1*x2, x3^2, x1^2*x3^2 ] [ x3, x2, x3^2, x1^2*x3^2 ] [ x3, x1, x3^2, x1^2*x3^2 ] [ x1*x2, x2, x3^2, x1^2*x3^2 ] [ x1^3*x2*x3*x1, x1*x2, x3^2, x1^2*x3^2 ] [ x1*x2*x3, x2, x3^2, x1^2*x3^2 ] [ x1^3*x2*x3*x1, x1, x3^2, x1^2*x3^2 ] [ x2*x1*x3, x2, x1*x2*x1*x2*x3^2, x1*x2*x1*x2 ] [ x2*x1*x3, x2*x1*x2, x1*x2*x1*x2*x3^2, x1*x2*x1*x2 ] [ x2*x1*x3, x1*x2, x1*x2*x1*x2*x3^2, x1*x2*x1*x2 ] [ x2, x2*x1*x2, x1*x2*x1*x2*x3^2, x1*x2*x1*x2 ] [ x2*x3, x2, x1*x2*x1*x2*x3^2, x1*x2*x1*x2 ] [ x1*x3, x2*x1*x2, x1*x2*x1*x2*x3^2, x1*x2*x1*x2 ] [ x2*x3, x1*x2, x1*x2*x1*x2*x3^2, x1*x2*x1*x2 ] [ x3, x1, x2^2, x1*x2^2*x3*x1*x3 ] [ x3, x2, x2^2, x1*x2^2*x3*x1*x3 ] [ x3, x1*x2, x2^2, x1*x2^2*x3*x1*x3 ] [ x1, x2, x2^2, x1*x2^2*x3*x1*x3 ] [ x2*x3, x1, x2^2, x1*x2^2*x3*x1*x3 ] [ x3*x1, x2, x2^2, x1*x2^2*x3*x1*x3 ] [ x2*x3, x1*x2, x2^2, x1*x2^2*x3*x1*x3 ] [ x3, x1, x2^2, x1*x2^2*x3*x1*x3 ] [ x3, x2, x2^2, x1*x2^2*x3*x1*x3 ] [ x3, x1*x2, x2^2, x1*x2^2*x3*x1*x3 ] [ x1, x2, x2^2, x1*x2^2*x3*x1*x3 ] [ x2*x3, x1, x2^2, x1*x2^2*x3*x1*x3 ] [ x3*x1, x2, x2^2, x1*x2^2*x3*x1*x3 ] [ x2*x3, x1*x2, x2^2, x1*x2^2*x3*x1*x3 ] [ x3, x1, x2^2, x1*x2^2*x3*x1*x3 ] [ x3, x2, x2^2, x1*x2^2*x3*x1*x3 ] [ x3, x1*x2, x2^2, x1*x2^2*x3*x1*x3 ] [ x1, x2, x2^2, x1*x2^2*x3*x1*x3 ] [ x2*x3, x1, x2^2, x1*x2^2*x3*x1*x3 ] [ x3*x1, x2, x2^2, x1*x2^2*x3*x1*x3 ] [ x2*x3, x1*x2, x2^2, x1*x2^2*x3*x1*x3 ] [ x3, x1*x2, x3^2, x1^2*x3^2 ] [ x3, x2, x3^2, x1^2*x3^2 ] [ x3, x1, x3^2, x1^2*x3^2 ] [ x1*x2, x2, x3^2, x1^2*x3^2 ] [ x1^3*x2*x3*x1, x1*x2, x3^2, x1^2*x3^2 ] [ x1*x2*x3, x2, x3^2, x1^2*x3^2 ] [ x1^3*x2*x3*x1, x1, x3^2, x1^2*x3^2 ] [ x3, x1, x3^2, x2*x3*x2*x3 ] [ x3, x1*x2, x3^2, x2*x3*x2*x3 ] [ x3, x2, x3^2, x2*x3*x2*x3 ] [ x1, x1*x2, x3^2, x2*x3*x2*x3 ] [ x3*x1*x2, x1, x3^2, x2*x3*x2*x3 ] [ x3*x1, x1*x2, x3^2, x2*x3*x2*x3 ] [ x3*x1*x2, x2, x3^2, x2*x3*x2*x3 ] [ x3, x1, x3^2, x2*x3*x2*x3 ] [ x3, x1*x2, x3^2, x2*x3*x2*x3 ] [ x3, x2, x3^2, x2*x3*x2*x3 ] [ x1, x1*x2, x3^2, x2*x3*x2*x3 ] [ x3*x1*x2, x1, x3^2, x2*x3*x2*x3 ] [ x3*x1, x1*x2, x3^2, x2*x3*x2*x3 ] [ x3*x1*x2, x2, x3^2, x2*x3*x2*x3 ] [ x2*x3, x1, x1^2, x1^3*x2*x1*x2 ] [ x2*x3, x2, x1^2, x1^3*x2*x1*x2 ] [ x2*x3, x1*x2, x1^2, x1^3*x2*x1*x2 ] [ x1, x2, x1^2, x1^3*x2*x1*x2 ] [ x3, x1, x1^2, x1^3*x2*x1*x2 ] [ x1^3*x2*x3, x2, x1^2, x1^3*x2*x1*x2 ] [ x3, x1*x2, x1^2, x1^3*x2*x1*x2 ] [ x2*x3, x1, x1^2, x1^3*x2*x1*x2 ] [ x2*x3, x2, x1^2, x1^3*x2*x1*x2 ] [ x2*x3, x1*x2, x1^2, x1^3*x2*x1*x2 ] [ x1, x2, x1^2, x1^3*x2*x1*x2 ] [ x3, x1, x1^2, x1^3*x2*x1*x2 ] [ x1^3*x2*x3, x2, x1^2, x1^3*x2*x1*x2 ] [ x3, x1*x2, x1^2, x1^3*x2*x1*x2 ] [ x1*x2*x1*x3, x1, x1^2, x1^3*x2*x1*x2 ] [ x1*x2*x1*x3, x2, x1^2, x1^3*x2*x1*x2 ] [ x1*x2*x1*x3, x1*x2, x1^2, x1^3*x2*x1*x2 ] [ x1, x2, x1^2, x1^3*x2*x1*x2 ] [ x1*x2*x1*x2*x3, x1, x1^2, x1^3*x2*x1*x2 ] [ x2*x1*x3, x2, x1^2, x1^3*x2*x1*x2 ] [ x1*x2*x1*x2*x3, x1*x2, x1^2, x1^3*x2*x1*x2 ] [ x1*x2*x1*x3, x1, x1^2, x1^3*x2*x1*x2 ] [ x1*x2*x1*x3, x2, x1^2, x1^3*x2*x1*x2 ] [ x1*x2*x1*x3, x1*x2, x1^2, x1^3*x2*x1*x2 ] [ x1, x2, x1^2, x1^3*x2*x1*x2 ] [ x1*x2*x1*x2*x3, x1, x1^2, x1^3*x2*x1*x2 ] [ x2*x1*x3, x2, x1^2, x1^3*x2*x1*x2 ] [ x1*x2*x1*x2*x3, x1*x2, x1^2, x1^3*x2*x1*x2 ] [ x2^2*x3, x1, x1^2*x2^2, x1^2 ] [ x2^2*x3, x1*x2, x1^2*x2^2, x1^2 ] [ x2^2*x3, x1^2*x2, x1^2*x2^2, x1^2 ] [ x1, x1*x2, x1^2*x2^2, x1^2 ] [ x1^3*x2*x3, x1, x1^2*x2^2, x1^2 ] [ x1^3*x2^2*x3, x1*x2, x1^2*x2^2, x1^2 ] [ x1^3*x2*x3, x1^2*x2, x1^2*x2^2, x1^2 ] [ x2^2*x3, x1, x1^2*x2^2, x1^2 ] [ x2^2*x3, x1*x2, x1^2*x2^2, x1^2 ] [ x2^2*x3, x1^2*x2, x1^2*x2^2, x1^2 ] [ x1, x1*x2, x1^2*x2^2, x1^2 ] [ x1^3*x2*x3, x1, x1^2*x2^2, x1^2 ] [ x1^3*x2^2*x3, x1*x2, x1^2*x2^2, x1^2 ] [ x1^3*x2*x3, x1^2*x2, x1^2*x2^2, x1^2 ] [ x1^2*x3, x1, x2^2, x1^2 ] [ x1^2*x3, x2, x2^2, x1^2 ] [ x1^2*x3, x1*x2, x2^2, x1^2 ] [ x1, x2, x2^2, x1^2 ] [ x1^2*x2^3*x3, x1, x2^2, x1^2 ] [ x1*x3, x2, x2^2, x1^2 ] [ x1^2*x2^3*x3, x1*x2, x2^2, x1^2 ] [ x2^2*x3, x3*x1*x3, x2^2, x1*x3*x1*x3 ] [ x2^2*x3, x1*x2, x2^2, x1*x3*x1*x3 ] [ x2^2*x3, x1*x2*x3*x1*x3, x2^2, x1*x3*x1*x3 ] [ x3*x1*x3, x1*x2, x2^2, x1*x3*x1*x3 ] [ x1*x2*x3, x3*x1*x3, x2^2, x1*x3*x1*x3 ] [ x1*x2^2*x3, x1*x2, x2^2, x1*x3*x1*x3 ] [ x1*x2*x3, x1*x2*x3*x1*x3, x2^2, x1*x3*x1*x3 ] [ x2^2*x3, x3*x1*x3, x2^2, x1*x3*x1*x3 ] [ x2^2*x3, x1*x2, x2^2, x1*x3*x1*x3 ] [ x2^2*x3, x1*x2*x3*x1*x3, x2^2, x1*x3*x1*x3 ] [ x3*x1*x3, x1*x2, x2^2, x1*x3*x1*x3 ] [ x1*x2*x3, x3*x1*x3, x2^2, x1*x3*x1*x3 ] [ x1*x2^2*x3, x1*x2, x2^2, x1*x3*x1*x3 ] [ x1*x2*x3, x1*x2*x3*x1*x3, x2^2, x1*x3*x1*x3 ] [ x1^2*x2^2*x3, x1, x2^2, x1^2 ] [ x1^2*x2^2*x3, x2, x2^2, x1^2 ] [ x1^2*x2^2*x3, x1*x2, x2^2, x1^2 ] [ x1, x2, x2^2, x1^2 ] [ x1^2*x2*x3, x1, x2^2, x1^2 ] [ x1*x2^2*x3, x2, x2^2, x1^2 ] [ x1^2*x2*x3, x1*x2, x2^2, x1^2 ] [ x2^2*x3, x3*x1*x3, x2^2, x1*x3*x1*x3 ] [ x2^2*x3, x1*x2, x2^2, x1*x3*x1*x3 ] [ x2^2*x3, x1*x2*x3*x1*x3, x2^2, x1*x3*x1*x3 ] [ x3*x1*x3, x1*x2, x2^2, x1*x3*x1*x3 ] [ x1*x2*x3, x3*x1*x3, x2^2, x1*x3*x1*x3 ] [ x1*x2^2*x3, x1*x2, x2^2, x1*x3*x1*x3 ] [ x1*x2*x3, x1*x2*x3*x1*x3, x2^2, x1*x3*x1*x3 ] [ x2^2*x3, x3*x1*x3, x2^2, x1*x3*x1*x3 ] [ x2^2*x3, x1*x2, x2^2, x1*x3*x1*x3 ] [ x2^2*x3, x1*x2*x3*x1*x3, x2^2, x1*x3*x1*x3 ] [ x3*x1*x3, x1*x2, x2^2, x1*x3*x1*x3 ] [ x1*x2*x3, x3*x1*x3, x2^2, x1*x3*x1*x3 ] [ x1*x2^2*x3, x1*x2, x2^2, x1*x3*x1*x3 ] [ x1*x2*x3, x1*x2*x3*x1*x3, x2^2, x1*x3*x1*x3 ] [ x3*x2, x1, x2*x3*x2*x3, x2^2 ] [ x3*x2, x2, x2*x3*x2*x3, x2^2 ] [ x3*x2, x1*x2, x2*x3*x2*x3, x2^2 ] [ x1, x2, x2*x3*x2*x3, x2^2 ] [ x2^2*x3, x1, x2*x3*x2*x3, x2^2 ] [ x1*x3*x2, x2, x2*x3*x2*x3, x2^2 ] [ x2^2*x3, x1*x2, x2*x3*x2*x3, x2^2 ] [ x3*x1, x1, x1*x3*x1*x3, x1^2 ] [ x3*x1, x2, x1*x3*x1*x3, x1^2 ] [ x3*x1, x1*x2, x1*x3*x1*x3, x1^2 ] [ x1, x2, x1*x3*x1*x3, x1^2 ] [ x2*x3*x1, x1, x1*x3*x1*x3, x1^2 ] [ x1^2*x3, x2, x1*x3*x1*x3, x1^2 ] [ x2*x3*x1, x1*x2, x1*x3*x1*x3, x1^2 ] [ x3, x2, x2^2, x1*x2*x1*x2^3 ] [ x3, x1, x2^2, x1*x2*x1*x2^3 ] [ x3, x2*x1, x2^2, x1*x2*x1*x2^3 ] [ x2, x1, x2^2, x1*x2*x1*x2^3 ] [ x1*x3, x2, x2^2, x1*x2*x1*x2^3 ] [ x2*x3, x1, x2^2, x1*x2*x1*x2^3 ] [ x1*x3, x2*x1, x2^2, x1*x2*x1*x2^3 ] [ x3, x1^3*x2, x2^2, x1^2 ] [ x3, x1, x2^2, x1^2 ] [ x3, x1^2*x2, x2^2, x1^2 ] [ x1^3*x2, x1, x2^2, x1^2 ] [ x1*x3, x1^3*x2, x2^2, x1^2 ] [ x1^3*x2*x3, x1, x2^2, x1^2 ] [ x1*x3, x1^2*x2, x2^2, x1^2 ] [ x4, x3, x1, x2^2, x1*x2^2*x3*x1*x3 ] [ x4, x3, x2, x2^2, x1*x2^2*x3*x1*x3 ] [ x4, x3, x1*x2, x2^2, x1*x2^2*x3*x1*x3 ] [ x4, x1, x2, x2^2, x1*x2^2*x3*x1*x3 ] [ x4, x2*x3, x1, x2^2, x1*x2^2*x3*x1*x3 ] [ x4, x3*x1, x2, x2^2, x1*x2^2*x3*x1*x3 ] [ x4, x2*x3, x1*x2, x2^2, x1*x2^2*x3*x1*x3 ] [ x3, x1, x2, x2^2, x1*x2^2*x3*x1*x3 ] [ x2*x4, x3, x1, x2^2, x1*x2^2*x3*x1*x3 ] [ x1*x4, x3, x2, x2^2, x1*x2^2*x3*x1*x3 ] [ x2*x4, x3, x1*x2, x2^2, x1*x2^2*x3*x1*x3 ] [ x3*x4, x1, x2, x2^2, x1*x2^2*x3*x1*x3 ] [ x2*x4, x2*x3, x1, x2^2, x1*x2^2*x3*x1*x3 ] [ x1*x4, x3*x1, x2, x2^2, x1*x2^2*x3*x1*x3 ] [ x2*x4, x2*x3, x1*x2, x2^2, x1*x2^2*x3*x1*x3 ] [ x4, x3, x1, x3^2, x2*x3*x2*x3 ] [ x4, x3, x1*x2, x3^2, x2*x3*x2*x3 ] [ x4, x3, x2, x3^2, x2*x3*x2*x3 ] [ x4, x1, x1*x2, x3^2, x2*x3*x2*x3 ] [ x4, x3*x1*x2, x1, x3^2, x2*x3*x2*x3 ] [ x4, x3*x1, x1*x2, x3^2, x2*x3*x2*x3 ] [ x4, x3*x1*x2, x2, x3^2, x2*x3*x2*x3 ] [ x3, x1, x1*x2, x3^2, x2*x3*x2*x3 ] [ x1*x2*x4, x3, x1, x3^2, x2*x3*x2*x3 ] [ x1*x4, x3, x1*x2, x3^2, x2*x3*x2*x3 ] [ x1*x2*x4, x3, x2, x3^2, x2*x3*x2*x3 ] [ x3*x4, x1, x1*x2, x3^2, x2*x3*x2*x3 ] [ x1*x2*x4, x3*x1*x2, x1, x3^2, x2*x3*x2*x3 ] [ x1*x4, x3*x1, x1*x2, x3^2, x2*x3*x2*x3 ] [ x1*x2*x4, x3*x1*x2, x2, x3^2, x2*x3*x2*x3 ] [ x4, x1^2*x3, x1, x2^2, x1^2 ] [ x4, x1^2*x3, x2, x2^2, x1^2 ] [ x4, x1^2*x3, x1*x2, x2^2, x1^2 ] [ x4, x1, x2, x2^2, x1^2 ] [ x4, x1^2*x2^3*x3, x1, x2^2, x1^2 ] [ x4, x1*x3, x2, x2^2, x1^2 ] [ x4, x1^2*x2^3*x3, x1*x2, x2^2, x1^2 ] [ x1^2*x3, x1, x2, x2^2, x1^2 ] [ x2*x4, x1^2*x3, x1, x2^2, x1^2 ] [ x1*x4, x1^2*x3, x2, x2^2, x1^2 ] [ x2*x4, x1^2*x3, x1*x2, x2^2, x1^2 ] [ x1^2*x3*x4, x1, x2, x2^2, x1^2 ] [ x2*x4, x1^2*x2^3*x3, x1, x2^2, x1^2 ] [ x1*x4, x1*x3, x2, x2^2, x1^2 ] [ x2*x4, x1^2*x2^3*x3, x1*x2, x2^2, x1^2 ] [ x4, x2^2*x3, x3*x1*x3, x2^2, x1*x3*x1*x3 ] [ x4, x2^2*x3, x1*x2, x2^2, x1*x3*x1*x3 ] [ x4, x2^2*x3, x1*x2*x3*x1*x3, x2^2, x1*x3*x1*x3 ] [ x4, x3*x1*x3, x1*x2, x2^2, x1*x3*x1*x3 ] [ x4, x1*x2*x3, x3*x1*x3, x2^2, x1*x3*x1*x3 ] [ x4, x1*x2^2*x3, x1*x2, x2^2, x1*x3*x1*x3 ] [ x4, x1*x2*x3, x1*x2*x3*x1*x3, x2^2, x1*x3*x1*x3 ] [ x2^2*x3, x3*x1*x3, x1*x2, x2^2, x1*x3*x1*x3 ] [ x1*x2*x4, x2^2*x3, x3*x1*x3, x2^2, x1*x3*x1*x3 ] [ x3*x1*x3*x4, x2^2*x3, x1*x2, x2^2, x1*x3*x1*x3 ] [ x1*x2*x4, x2^2*x3, x1*x2*x3*x1*x3, x2^2, x1*x3*x1*x3 ] [ x2^2*x3*x4, x3*x1*x3, x1*x2, x2^2, x1*x3*x1*x3 ] [ x1*x2*x4, x1*x2*x3, x3*x1*x3, x2^2, x1*x3*x1*x3 ] [ x3*x1*x3*x4, x1*x2^2*x3, x1*x2, x2^2, x1*x3*x1*x3 ] [ x1*x2*x4, x1*x2*x3, x1*x2*x3*x1*x3, x2^2, x1*x3*x1*x3 ] [ x2*x1*x2*x3*x4*x3, x1, x2, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x1*x2*x3*x4*x3, x1, x1*x2*x1*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x1*x2*x3*x4*x3, x1, x1*x2*x1*x2*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x1*x2*x3*x4*x3, x2, x1*x2*x1*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x1*x2*x3*x4*x3, x2*x1*x4*x3*x4, x2, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x1*x2*x3*x4*x3, x1*x2, x1*x2*x1*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x1*x2*x3*x4*x3, x2*x1*x4*x3*x4, x1*x2*x1*x2*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x1, x2, x1*x2*x1*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x1*x4*x3, x1, x2, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x1*x2*x3*x4*x3, x1, x1*x2*x1*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x1*x4*x3, x1, x1*x2*x1*x2*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x1*x2*x1*x2*x3*x4*x3, x2, x1*x2*x1*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x1*x4*x3, x2*x1*x4*x3*x4, x2, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x1*x2*x3*x4*x3, x1*x2, x1*x2*x1*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x1*x4*x3, x2*x1*x4*x3*x4, x1*x2*x1*x2*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x1*x2*x3*x4*x3, x1, x2, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x1*x2*x3*x4*x3, x1, x1*x2*x1*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x1*x2*x3*x4*x3, x1, x1*x2*x1*x2*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x1*x2*x3*x4*x3, x2, x1*x2*x1*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x1*x2*x3*x4*x3, x2*x1*x4*x3*x4, x2, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x1*x2*x3*x4*x3, x1*x2, x1*x2*x1*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x1*x2*x3*x4*x3, x2*x1*x4*x3*x4, x1*x2*x1*x2*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x1, x2, x1*x2*x1*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x1*x4*x3, x1, x2, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x1*x2*x3*x4*x3, x1, x1*x2*x1*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x1*x4*x3, x1, x1*x2*x1*x2*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x1*x2*x1*x2*x3*x4*x3, x2, x1*x2*x1*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x1*x4*x3, x2*x1*x4*x3*x4, x2, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x1*x2*x3*x4*x3, x1*x2, x1*x2*x1*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x1*x4*x3, x2*x1*x4*x3*x4, x1*x2*x1*x2*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x1*x2*x3*x4*x3, x1, x2, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x1*x2*x3*x4*x3, x1, x1*x2*x1*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x1*x2*x3*x4*x3, x1, x1*x2*x1*x2*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x1*x2*x3*x4*x3, x2, x1*x2*x1*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x1*x2*x3*x4*x3, x2*x1*x4*x3*x4, x2, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x1*x2*x3*x4*x3, x1*x2, x1*x2*x1*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x1*x2*x3*x4*x3, x2*x1*x4*x3*x4, x1*x2*x1*x2*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x1, x2, x1*x2*x1*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x1*x4*x3, x1, x2, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x1*x2*x3*x4*x3, x1, x1*x2*x1*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x1*x4*x3, x1, x1*x2*x1*x2*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x1*x2*x1*x2*x3*x4*x3, x2, x1*x2*x1*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x1*x4*x3, x2*x1*x4*x3*x4, x2, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x1*x2*x3*x4*x3, x1*x2, x1*x2*x1*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x1*x4*x3, x2*x1*x4*x3*x4, x1*x2*x1*x2*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x1*x3^2*x4, x1, x2, x3^2, x1*x2*x1*x2 ] [ x1*x3^2*x4, x1, x2*x3, x3^2, x1*x2*x1*x2 ] [ x1*x3^2*x4, x1, x3, x3^2, x1*x2*x1*x2 ] [ x1*x3^2*x4, x2, x2*x3, x3^2, x1*x2*x1*x2 ] [ x1*x3^2*x4, x1*x2*x3, x2, x3^2, x1*x2*x1*x2 ] [ x1*x3^2*x4, x1*x2, x2*x3, x3^2, x1*x2*x1*x2 ] [ x1*x3^2*x4, x1*x2*x3, x3, x3^2, x1*x2*x1*x2 ] [ x1, x2, x2*x3, x3^2, x1*x2*x1*x2 ] [ x1*x2*x3*x4, x1, x2, x3^2, x1*x2*x1*x2 ] [ x2*x1*x3^2*x4, x1, x2*x3, x3^2, x1*x2*x1*x2 ] [ x1*x2*x3*x4, x1, x3, x3^2, x1*x2*x1*x2 ] [ x3^2*x4, x2, x2*x3, x3^2, x1*x2*x1*x2 ] [ x1*x2*x3*x4, x1*x2*x3, x2, x3^2, x1*x2*x1*x2 ] [ x2*x1*x3^2*x4, x1*x2, x2*x3, x3^2, x1*x2*x1*x2 ] [ x1*x2*x3*x4, x1*x2*x3, x3, x3^2, x1*x2*x1*x2 ] [ x2*x1*x2*x3*x4*x3, x1, x2, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x1*x2*x3*x4*x3, x1, x1*x2*x1*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x1*x2*x3*x4*x3, x1, x1*x2*x1*x2*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x1*x2*x3*x4*x3, x2, x1*x2*x1*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x1*x2*x3*x4*x3, x2*x1*x4*x3*x4, x2, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x1*x2*x3*x4*x3, x1*x2, x1*x2*x1*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x1*x2*x3*x4*x3, x2*x1*x4*x3*x4, x1*x2*x1*x2*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x1, x2, x1*x2*x1*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x1*x4*x3, x1, x2, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x1*x2*x3*x4*x3, x1, x1*x2*x1*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x1*x4*x3, x1, x1*x2*x1*x2*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x1*x2*x1*x2*x3*x4*x3, x2, x1*x2*x1*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x1*x4*x3, x2*x1*x4*x3*x4, x2, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x1*x2*x3*x4*x3, x1*x2, x1*x2*x1*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x1*x4*x3, x2*x1*x4*x3*x4, x1*x2*x1*x2*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x1*x2*x3*x4*x3, x1, x2, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x1*x2*x3*x4*x3, x1, x1*x2*x1*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x1*x2*x3*x4*x3, x1, x1*x2*x1*x2*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x1*x2*x3*x4*x3, x2, x1*x2*x1*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x1*x2*x3*x4*x3, x2*x1*x4*x3*x4, x2, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x1*x2*x3*x4*x3, x1*x2, x1*x2*x1*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x1*x2*x3*x4*x3, x2*x1*x4*x3*x4, x1*x2*x1*x2*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x1, x2, x1*x2*x1*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x1*x4*x3, x1, x2, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x1*x2*x3*x4*x3, x1, x1*x2*x1*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x1*x4*x3, x1, x1*x2*x1*x2*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x1*x2*x1*x2*x3*x4*x3, x2, x1*x2*x1*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x1*x4*x3, x2*x1*x4*x3*x4, x2, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x1*x2*x3*x4*x3, x1*x2, x1*x2*x1*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2*x1*x4*x3, x2*x1*x4*x3*x4, x1*x2*x1*x2*x4*x3*x4, x1*x2*x1*x2*x3*x4*x3*x4, x1*x2*x1*x2 ] [ x2, x2^2 ] [ x1, x2^2 ] [ x1*x2, x2^2 ] [ x2, x2^2 ] [ x1, x2^2 ] [ x1*x2, x2^2 ] [ x1*x2, x2^2 ] [ x1, x2^2 ] [ x2, x2^2 ] gap> LogTo();