GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
gap> RequirePackage("carat"); true gap> names := []; [ ] gap> GROUPS := []; [ ] gap> R := CaratReadBravaisFile("ordnung.16/(2)^1(4)^2(8)^2/group.1138"); 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> P1 := Group(R.generators); <matrix group with 3 generators> gap> Append(names,["ordnung.16/(2)^1(4)^2(8)^2/words.group.1138"]); gap> Append(GROUPS,[P1]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^2(4)^2(32)^1/group.1139"); 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> P2 := Group(R.generators); <matrix group with 3 generators> gap> Append(names,["ordnung.16/(2)^2(4)^2(32)^1/words.group.1139"]); gap> Append(GROUPS,[P2]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^2(4)^2(8)^1/group.1140"); 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> P3 := Group(R.generators); <matrix group with 3 generators> gap> Append(names,["ordnung.16/(2)^2(4)^2(8)^1/words.group.1140"]); gap> Append(GROUPS,[P3]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^2(4)^2(8)^1/group.1141"); 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> P4 := Group(R.generators); <matrix group with 3 generators> gap> Append(names,["ordnung.16/(2)^2(4)^2(8)^1/words.group.1141"]); gap> Append(GROUPS,[P4]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^2(4)^2(8)^1/group.1142"); 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> P5 := Group(R.generators); <matrix group with 3 generators> gap> Append(names,["ordnung.16/(2)^2(4)^2(8)^1/words.group.1142"]); gap> Append(GROUPS,[P5]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^2(4)^2(8)^1/group.1143"); 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> P6 := Group(R.generators); <matrix group with 3 generators> gap> Append(names,["ordnung.16/(2)^2(4)^2(8)^1/words.group.1143"]); gap> Append(GROUPS,[P6]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^2(4)^2(8)^1/group.1144"); 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); <matrix group with 3 generators> gap> Append(names,["ordnung.16/(2)^2(4)^2(8)^1/words.group.1144"]); gap> Append(GROUPS,[P7]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^2(4)^2(8)^1/group.1145"); 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> P8 := Group(R.generators); <matrix group with 3 generators> gap> Append(names,["ordnung.16/(2)^2(4)^2(8)^1/words.group.1145"]); gap> Append(GROUPS,[P8]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^4(4)^2(32)^1/group.1146"); 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); <matrix group with 3 generators> gap> Append(names,["ordnung.16/(2)^4(4)^2(32)^1/words.group.1146"]); gap> Append(GROUPS,[P9]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^4(4)^2(32)^1/group.1147"); 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> P10 := Group(R.generators); <matrix group with 3 generators> gap> Append(names,["ordnung.16/(2)^4(4)^2(32)^1/words.group.1147"]); gap> Append(GROUPS,[P10]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^4(4)^2(32)^1/group.1148"); 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> P11 := Group(R.generators); <matrix group with 3 generators> gap> Append(names,["ordnung.16/(2)^4(4)^2(32)^1/words.group.1148"]); gap> Append(GROUPS,[P11]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^4(4)^2(32)^1/group.1149"); 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); <matrix group with 3 generators> gap> Append(names,["ordnung.16/(2)^4(4)^2(32)^1/words.group.1149"]); gap> Append(GROUPS,[P12]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^4(4)^2(32)^1/group.1150"); 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); <matrix group with 3 generators> gap> Append(names,["ordnung.16/(2)^4(4)^2(32)^1/words.group.1150"]); gap> Append(GROUPS,[P13]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^4(4)^2(32)^1/group.1151"); 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); <matrix group with 3 generators> gap> Append(names,["ordnung.16/(2)^4(4)^2(32)^1/words.group.1151"]); gap> Append(GROUPS,[P14]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^4(4)^2(32)^1/group.1152"); 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> P15 := Group(R.generators); <matrix group with 3 generators> gap> Append(names,["ordnung.16/(2)^4(4)^2(32)^1/words.group.1152"]); gap> Append(GROUPS,[P15]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^4(4)^2(32)^1/group.1153"); 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> P16 := Group(R.generators); <matrix group with 3 generators> gap> Append(names,["ordnung.16/(2)^4(4)^2(32)^1/words.group.1153"]); gap> Append(GROUPS,[P16]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^4(4)^2(32)^1/group.1154"); 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> P17 := Group(R.generators); <matrix group with 3 generators> gap> Append(names,["ordnung.16/(2)^4(4)^2(32)^1/words.group.1154"]); gap> Append(GROUPS,[P17]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^4(4)^2(32)^1/group.1155"); 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> P18 := Group(R.generators); <matrix group with 3 generators> gap> Append(names,["ordnung.16/(2)^4(4)^2(32)^1/words.group.1155"]); gap> Append(GROUPS,[P18]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^4(4)^2(32)^1/group.1156"); 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); <matrix group with 3 generators> gap> Append(names,["ordnung.16/(2)^4(4)^2(32)^1/words.group.1156"]); gap> Append(GROUPS,[P19]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^4(4)^2(32)^1/group.1157"); 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> P20 := Group(R.generators); <matrix group with 3 generators> gap> Append(names,["ordnung.16/(2)^4(4)^2(32)^1/words.group.1157"]); gap> Append(GROUPS,[P20]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^4(4)^2(32)^1/group.1158"); 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); <matrix group with 3 generators> gap> Append(names,["ordnung.16/(2)^4(4)^2(32)^1/words.group.1158"]); gap> Append(GROUPS,[P21]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^4(4)^2(32)^1/group.1159"); 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); <matrix group with 3 generators> gap> Append(names,["ordnung.16/(2)^4(4)^2(32)^1/words.group.1159"]); gap> Append(GROUPS,[P22]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^4(8)^2(32)^1/group.1160"); 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> P23 := Group(R.generators); <matrix group with 3 generators> gap> Append(names,["ordnung.16/(2)^4(8)^2(32)^1/words.group.1160"]); gap> Append(GROUPS,[P23]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^4(8)^2(32)^1/group.1161"); 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); <matrix group with 3 generators> gap> Append(names,["ordnung.16/(2)^4(8)^2(32)^1/words.group.1161"]); gap> Append(GROUPS,[P24]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^4(8)^3/group.1162"); 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); <matrix group with 3 generators> gap> Append(names,["ordnung.16/(2)^4(8)^3/words.group.1162"]); gap> Append(GROUPS,[P25]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^4(8)^3/group.1163"); 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> P26 := Group(R.generators); <matrix group with 3 generators> gap> Append(names,["ordnung.16/(2)^4(8)^3/words.group.1163"]); gap> Append(GROUPS,[P26]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^4(8)^3/group.1164"); 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> P27 := Group(R.generators); <matrix group with 3 generators> gap> Append(names,["ordnung.16/(2)^4(8)^3/words.group.1164"]); gap> Append(GROUPS,[P27]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^4(8)^3/group.1165"); 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> P28 := Group(R.generators); <matrix group with 3 generators> gap> Append(names,["ordnung.16/(2)^4(8)^3/words.group.1165"]); gap> Append(GROUPS,[P28]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^4(8)^3/group.1166"); 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> P29 := Group(R.generators); <matrix group with 3 generators> gap> Append(names,["ordnung.16/(2)^4(8)^3/words.group.1166"]); gap> Append(GROUPS,[P29]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^4(8)^3/group.1167"); 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> P30 := Group(R.generators); <matrix group with 3 generators> gap> Append(names,["ordnung.16/(2)^4(8)^3/words.group.1167"]); gap> Append(GROUPS,[P30]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^4(8)^3/group.1168"); 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> P31 := Group(R.generators); <matrix group with 3 generators> gap> Append(names,["ordnung.16/(2)^4(8)^3/words.group.1168"]); gap> Append(GROUPS,[P31]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^4(8)^3/group.1169"); 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> P32 := Group(R.generators); <matrix group with 3 generators> gap> Append(names,["ordnung.16/(2)^4(8)^3/words.group.1169"]); gap> Append(GROUPS,[P32]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^4(8)^3/group.1170"); 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> P33 := Group(R.generators); <matrix group with 3 generators> gap> Append(names,["ordnung.16/(2)^4(8)^3/words.group.1170"]); gap> Append(GROUPS,[P33]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^4(8)^3/group.1171"); 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> P34 := Group(R.generators); <matrix group with 3 generators> gap> Append(names,["ordnung.16/(2)^4(8)^3/words.group.1171"]); gap> Append(GROUPS,[P34]); gap> R := CaratReadBravaisFile("ordnung.16/(2)^4(8)^3/group.1172"); 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> P35 := Group(R.generators); <matrix group with 3 generators> gap> Append(names,["ordnung.16/(2)^4(8)^3/words.group.1172"]); gap> Append(GROUPS,[P35]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^2(4)^2(8)^1/group.1173"); 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> P36 := Group(R.generators); <matrix group with 4 generators> gap> Append(names,["ordnung.32/(2)^2(4)^2(8)^1/words.group.1173"]); gap> Append(GROUPS,[P36]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^2(32)^1/group.1174"); 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); <matrix group with 4 generators> gap> Append(names,["ordnung.32/(2)^4(4)^2(32)^1/words.group.1174"]); gap> Append(GROUPS,[P37]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^2(32)^1/group.1175"); 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> P38 := Group(R.generators); <matrix group with 4 generators> gap> Append(names,["ordnung.32/(2)^4(4)^2(32)^1/words.group.1175"]); gap> Append(GROUPS,[P38]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^2(8)^1/group.1176"); 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> P39 := Group(R.generators); <matrix group with 4 generators> gap> Append(names,["ordnung.32/(2)^4(4)^2(8)^1/words.group.1176"]); gap> Append(GROUPS,[P39]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^2(8)^1/group.1177"); 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); <matrix group with 4 generators> gap> Append(names,["ordnung.32/(2)^4(4)^2(8)^1/words.group.1177"]); gap> Append(GROUPS,[P40]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^2(8)^1/group.1178"); 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); <matrix group with 4 generators> gap> Append(names,["ordnung.32/(2)^4(4)^2(8)^1/words.group.1178"]); gap> Append(GROUPS,[P41]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^2(8)^1/group.1179"); 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); <matrix group with 4 generators> gap> Append(names,["ordnung.32/(2)^4(4)^2(8)^1/words.group.1179"]); gap> Append(GROUPS,[P42]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^2(8)^1/group.1180"); 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> P43 := Group(R.generators); <matrix group with 4 generators> gap> Append(names,["ordnung.32/(2)^4(4)^2(8)^1/words.group.1180"]); gap> Append(GROUPS,[P43]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^2(8)^1/group.1181"); 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> P44 := Group(R.generators); <matrix group with 4 generators> gap> Append(names,["ordnung.32/(2)^4(4)^2(8)^1/words.group.1181"]); gap> Append(GROUPS,[P44]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^2(8)^1/group.1182"); 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> P45 := Group(R.generators); <matrix group with 4 generators> gap> Append(names,["ordnung.32/(2)^4(4)^2(8)^1/words.group.1182"]); gap> Append(GROUPS,[P45]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^2(8)^1/group.1183"); 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); <matrix group with 4 generators> gap> Append(names,["ordnung.32/(2)^4(4)^2(8)^1/words.group.1183"]); gap> Append(GROUPS,[P46]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(4)^2(8)^1/group.1184"); 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> P47 := Group(R.generators); <matrix group with 4 generators> gap> Append(names,["ordnung.32/(2)^4(4)^2(8)^1/words.group.1184"]); gap> Append(GROUPS,[P47]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(8)^3/group.1185"); 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> P48 := Group(R.generators); <matrix group with 4 generators> gap> Append(names,["ordnung.32/(2)^4(8)^3/words.group.1185"]); gap> Append(GROUPS,[P48]); gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(8)^3/group.1186"); 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> P49 := Group(R.generators); <matrix group with 4 generators> gap> Append(names,["ordnung.32/(2)^4(8)^3/words.group.1186"]); gap> Append(GROUPS,[P49]); gap> R := CaratReadBravaisFile("ordnung.64/(2)^4(4)^2(8)^1/group.1187"); 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> P50 := Group(R.generators); <matrix group with 5 generators> gap> Append(names,["ordnung.64/(2)^4(4)^2(8)^1/words.group.1187"]); gap> Append(GROUPS,[P50]); gap> R := CaratReadBravaisFile("ordnung.8/(2)^1(4)^2(8)^2/min.228"); 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> P51 := Group(R.generators); <matrix group with 2 generators> gap> Append(names,["ordnung.8/(2)^1(4)^2(8)^2/words.min.228"]); gap> Append(GROUPS,[P51]); gap> R := CaratReadBravaisFile("ordnung.8/(2)^1(4)^2(8)^2/min.229"); 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 ] ] ], size := 8 ) gap> P52 := Group(R.generators); <matrix group with 2 generators> gap> Append(names,["ordnung.8/(2)^1(4)^2(8)^2/words.min.229"]); gap> Append(GROUPS,[P52]); gap> R := CaratReadBravaisFile("ordnung.8/(2)^1(4)^2(8)^2/min.230"); 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 ] ] ], size := 8 ) gap> P53 := Group(R.generators); <matrix group with 2 generators> gap> Append(names,["ordnung.8/(2)^1(4)^2(8)^2/words.min.230"]); gap> Append(GROUPS,[P53]); gap> R := CaratReadBravaisFile("ordnung.8/(2)^2(4)^2(32)^1/min.231"); 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 ] ] ], size := 8 ) gap> P54 := Group(R.generators); <matrix group with 2 generators> gap> Append(names,["ordnung.8/(2)^2(4)^2(32)^1/words.min.231"]); gap> Append(GROUPS,[P54]); gap> R := CaratReadBravaisFile("ordnung.8/(2)^2(4)^2(32)^1/min.232"); 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 ] ] ], size := 8 ) gap> P55 := Group(R.generators); <matrix group with 2 generators> gap> Append(names,["ordnung.8/(2)^2(4)^2(32)^1/words.min.232"]); gap> Append(GROUPS,[P55]); gap> R := CaratReadBravaisFile("ordnung.8/(2)^2(4)^2(32)^1/min.233"); 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> P56 := Group(R.generators); <matrix group with 2 generators> gap> Append(names,["ordnung.8/(2)^2(4)^2(32)^1/words.min.233"]); gap> Append(GROUPS,[P56]); gap> R := CaratReadBravaisFile("ordnung.8/(2)^2(4)^2(32)^1/min.234"); 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> P57 := Group(R.generators); <matrix group with 2 generators> gap> Append(names,["ordnung.8/(2)^2(4)^2(32)^1/words.min.234"]); gap> Append(GROUPS,[P57]); gap> R := CaratReadBravaisFile("ordnung.8/(2)^4(8)^2(32)^1/min.235"); 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> P58 := Group(R.generators); <matrix group with 2 generators> gap> Append(names,["ordnung.8/(2)^4(8)^2(32)^1/words.min.235"]); gap> Append(GROUPS,[P58]); gap> R := CaratReadBravaisFile("ordnung.8/(2)^4(8)^2(32)^1/min.236"); 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> P59 := Group(R.generators); <matrix group with 2 generators> gap> Append(names,["ordnung.8/(2)^4(8)^2(32)^1/words.min.236"]); gap> Append(GROUPS,[P59]); gap> R := CaratReadBravaisFile("ordnung.8/(2)^4(8)^2(32)^1/min.237"); 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> P60 := Group(R.generators); <matrix group with 2 generators> gap> Append(names,["ordnung.8/(2)^4(8)^2(32)^1/words.min.237"]); gap> Append(GROUPS,[P60]); gap> R := CaratReadBravaisFile("ordnung.8/(2)^4(8)^2(32)^1/min.238"); 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 ] ] ], size := 8 ) gap> P61 := Group(R.generators); <matrix group with 2 generators> gap> Append(names,["ordnung.8/(2)^4(8)^2(32)^1/words.min.238"]); gap> Append(GROUPS,[P61]); gap> R := CaratReadBravaisFile("ordnung.8/(2)^4(8)^2(32)^1/min.239"); 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 ] ] ], size := 8 ) gap> P62 := Group(R.generators); <matrix group with 2 generators> gap> Append(names,["ordnung.8/(2)^4(8)^2(32)^1/words.min.239"]); gap> Append(GROUPS,[P62]); gap> R := CaratReadBravaisFile("ordnung.8/(2)^4(8)^2(32)^1/min.240"); 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> P63 := Group(R.generators); <matrix group with 2 generators> gap> Append(names,["ordnung.8/(2)^4(8)^2(32)^1/words.min.240"]); gap> Append(GROUPS,[P63]); gap> R := CaratReadBravaisFile("ordnung.8/(2)^4(8)^2(32)^1/min.241"); 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> P64 := Group(R.generators); <matrix group with 2 generators> gap> Append(names,["ordnung.8/(2)^4(8)^2(32)^1/words.min.241"]); gap> Append(GROUPS,[P64]); 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 ] ] ]), 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 ] ], [ [ 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([ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 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([ [ [ 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([ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 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 ], [ 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 ] ], [ [ 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([ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 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([ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 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, 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"ordnung.16/(2)^2(4)^2(32)^1/words.group.1139", "ordnung.16/(2)^2(4)^2(8)^1/words.group.1140", "ordnung.16/(2)^2(4)^2(8)^1/words.group.1141", "ordnung.16/(2)^2(4)^2(8)^1/words.group.1142", "ordnung.16/(2)^2(4)^2(8)^1/words.group.1143", "ordnung.16/(2)^2(4)^2(8)^1/words.group.1144", "ordnung.16/(2)^2(4)^2(8)^1/words.group.1145", "ordnung.16/(2)^4(4)^2(32)^1/words.group.1146", "ordnung.16/(2)^4(4)^2(32)^1/words.group.1147", "ordnung.16/(2)^4(4)^2(32)^1/words.group.1148", "ordnung.16/(2)^4(4)^2(32)^1/words.group.1149", "ordnung.16/(2)^4(4)^2(32)^1/words.group.1150", "ordnung.16/(2)^4(4)^2(32)^1/words.group.1151", "ordnung.16/(2)^4(4)^2(32)^1/words.group.1152", "ordnung.16/(2)^4(4)^2(32)^1/words.group.1153", "ordnung.16/(2)^4(4)^2(32)^1/words.group.1154", "ordnung.16/(2)^4(4)^2(32)^1/words.group.1155", "ordnung.16/(2)^4(4)^2(32)^1/words.group.1156", "ordnung.16/(2)^4(4)^2(32)^1/words.group.1157", "ordnung.16/(2)^4(4)^2(32)^1/words.group.1158", "ordnung.16/(2)^4(4)^2(32)^1/words.group.1159", "ordnung.16/(2)^4(8)^2(32)^1/words.group.1160", "ordnung.16/(2)^4(8)^2(32)^1/words.group.1161", "ordnung.16/(2)^4(8)^3/words.group.1162", "ordnung.16/(2)^4(8)^3/words.group.1163", "ordnung.16/(2)^4(8)^3/words.group.1164", "ordnung.16/(2)^4(8)^3/words.group.1165", "ordnung.16/(2)^4(8)^3/words.group.1166", "ordnung.16/(2)^4(8)^3/words.group.1167", "ordnung.16/(2)^4(8)^3/words.group.1168", "ordnung.16/(2)^4(8)^3/words.group.1169", "ordnung.16/(2)^4(8)^3/words.group.1170", "ordnung.16/(2)^4(8)^3/words.group.1171", "ordnung.16/(2)^4(8)^3/words.group.1172", "ordnung.32/(2)^2(4)^2(8)^1/words.group.1173", "ordnung.32/(2)^4(4)^2(32)^1/words.group.1174", "ordnung.32/(2)^4(4)^2(32)^1/words.group.1175", "ordnung.32/(2)^4(4)^2(8)^1/words.group.1176", "ordnung.32/(2)^4(4)^2(8)^1/words.group.1177", "ordnung.32/(2)^4(4)^2(8)^1/words.group.1178", "ordnung.32/(2)^4(4)^2(8)^1/words.group.1179", "ordnung.32/(2)^4(4)^2(8)^1/words.group.1180", "ordnung.32/(2)^4(4)^2(8)^1/words.group.1181", "ordnung.32/(2)^4(4)^2(8)^1/words.group.1182", "ordnung.32/(2)^4(4)^2(8)^1/words.group.1183", "ordnung.32/(2)^4(4)^2(8)^1/words.group.1184", "ordnung.32/(2)^4(8)^3/words.group.1185", "ordnung.32/(2)^4(8)^3/words.group.1186", "ordnung.64/(2)^4(4)^2(8)^1/words.group.1187", "ordnung.8/(2)^1(4)^2(8)^2/words.min.228", "ordnung.8/(2)^1(4)^2(8)^2/words.min.229", "ordnung.8/(2)^1(4)^2(8)^2/words.min.230", "ordnung.8/(2)^2(4)^2(32)^1/words.min.231", "ordnung.8/(2)^2(4)^2(32)^1/words.min.232", "ordnung.8/(2)^2(4)^2(32)^1/words.min.233", "ordnung.8/(2)^2(4)^2(32)^1/words.min.234", "ordnung.8/(2)^4(8)^2(32)^1/words.min.235", "ordnung.8/(2)^4(8)^2(32)^1/words.min.236", "ordnung.8/(2)^4(8)^2(32)^1/words.min.237", "ordnung.8/(2)^4(8)^2(32)^1/words.min.238", "ordnung.8/(2)^4(8)^2(32)^1/words.min.239", "ordnung.8/(2)^4(8)^2(32)^1/words.min.240", "ordnung.8/(2)^4(8)^2(32)^1/words.min.241" ] gap> Size(GROUPS); 64 gap> Size(names); 64 gap> Read("../../TGROUPS.GAP"); gap> for i in [1..Size(GROUPS)] do > SubgroupWords(GROUPS[i], names[i]); > od; [ 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 ] [ 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, 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 ] [ x2*x3, x2, x3^2 ] [ x2*x3, x1, x3^2 ] [ x2*x3, x1*x2, x3^2 ] [ x2, x1, x3^2 ] [ x1*x2*x3, x2, x3^2 ] [ x3, x1, x3^2 ] [ x1*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 ] [ 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 ] [ 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, 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, 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 ] [ x1*x3, x1, x2*x3*x2*x3 ] [ x1*x3, x3*x2*x3, x2*x3*x2*x3 ] [ x1*x3, x1*x3*x2*x3, x2*x3*x2*x3 ] [ x1, x3*x2*x3, x2*x3*x2*x3 ] [ x1*x2*x3, x1, x2*x3*x2*x3 ] [ x3, x3*x2*x3, x2*x3*x2*x3 ] [ x1*x2*x3, x1*x3*x2*x3, x2*x3*x2*x3 ] [ 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 ] [ x1*x3*x1, x3*x1*x3, x1*x3*x1*x3 ] [ x1*x3*x1, x2, x1*x3*x1*x3 ] [ x1*x3*x1, x2*x3*x1*x3, x1*x3*x1*x3 ] [ x3*x1*x3, x2, x1*x3*x1*x3 ] [ x1*x2*x3*x1, x3*x1*x3, x1*x3*x1*x3 ] [ x3*x1, x2, x1*x3*x1*x3 ] [ x1*x2*x3*x1, x2*x3*x1*x3, x1*x3*x1*x3 ] [ x1*x3*x1, x3*x1*x3, x1*x3*x1*x3 ] [ x1*x3*x1, x2, x1*x3*x1*x3 ] [ x1*x3*x1, x2*x3*x1*x3, x1*x3*x1*x3 ] [ x3*x1*x3, x2, x1*x3*x1*x3 ] [ x1*x2*x3*x1, x3*x1*x3, x1*x3*x1*x3 ] [ x3*x1, x2, x1*x3*x1*x3 ] [ x1*x2*x3*x1, x2*x3*x1*x3, x1*x3*x1*x3 ] [ 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 ] [ x1*x2*x1*x2*x3, x2, x1*x2*x1*x2 ] [ x1*x2*x1*x2*x3, x1, x1*x2*x1*x2 ] [ x1*x2*x1*x2*x3, x2*x1, x1*x2*x1*x2 ] [ x2, x1, x1*x2*x1*x2 ] [ x2*x1*x2*x3, x2, x1*x2*x1*x2 ] [ x1*x2*x1*x3, x1, x1*x2*x1*x2 ] [ x2*x1*x2*x3, x2*x1, x1*x2*x1*x2 ] [ x1*x2*x1*x2*x3, x2, x1*x2*x1*x2 ] [ x1*x2*x1*x2*x3, x1, x1*x2*x1*x2 ] [ x1*x2*x1*x2*x3, x2*x1, x1*x2*x1*x2 ] [ x2, x1, x1*x2*x1*x2 ] [ x2*x1*x2*x3, x2, x1*x2*x1*x2 ] [ x1*x2*x1*x3, x1, x1*x2*x1*x2 ] [ x2*x1*x2*x3, x2*x1, x1*x2*x1*x2 ] [ 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, 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 ] [ x3, x1, x2*x3*x2*x3 ] [ x3, x2, x2*x3*x2*x3 ] [ x3, x1*x2, x2*x3*x2*x3 ] [ x1, x2, x2*x3*x2*x3 ] [ x3*x2, x1, x2*x3*x2*x3 ] [ x1*x3, x2, x2*x3*x2*x3 ] [ x3*x2, x1*x2, x2*x3*x2*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 ] [ 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, 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 ] [ x1*x3*x1, x3*x1*x3, x1*x3*x1*x3 ] [ x1*x3*x1, x2, x1*x3*x1*x3 ] [ x1*x3*x1, x2*x3*x1*x3, x1*x3*x1*x3 ] [ x3*x1*x3, x2, x1*x3*x1*x3 ] [ x1*x2*x3*x1, x3*x1*x3, x1*x3*x1*x3 ] [ x3*x1, x2, x1*x3*x1*x3 ] [ x1*x2*x3*x1, x2*x3*x1*x3, x1*x3*x1*x3 ] [ 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*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, 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 ] [ x1*x3*x1, x3*x1*x3, x1*x3*x1*x3 ] [ x1*x3*x1, x2, x1*x3*x1*x3 ] [ x1*x3*x1, x2*x3*x1*x3, x1*x3*x1*x3 ] [ x3*x1*x3, x2, x1*x3*x1*x3 ] [ x1*x2*x3*x1, x3*x1*x3, x1*x3*x1*x3 ] [ x3*x1, x2, x1*x3*x1*x3 ] [ x1*x2*x3*x1, x2*x3*x1*x3, x1*x3*x1*x3 ] [ 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 ] [ x3, x1, x3^2 ] [ x3, x2, x3^2 ] [ x3, x1*x2, x3^2 ] [ x1, x2, x3^2 ] [ x2*x3, x1, x3^2 ] [ x3*x1, x2, x3^2 ] [ x2*x3, x1*x2, x3^2 ] [ x3, x1, x3^2 ] [ x3, x2, x3^2 ] [ x3, x1*x2, x3^2 ] [ x1, x2, x3^2 ] [ x2*x3, x1, x3^2 ] [ x3*x1, x2, x3^2 ] [ x2*x3, x1*x2, x3^2 ] [ x3, x2, x2^2 ] [ x3, x1, x2^2 ] [ x3, x2*x1, x2^2 ] [ x2, x1, x2^2 ] [ x1*x3, x2, x2^2 ] [ x2*x3, x1, x2^2 ] [ x1*x3, x2*x1, x2^2 ] [ x3, x2, x1^2 ] [ x3, x1, x1^2 ] [ x3, x1^3*x2, x1^2 ] [ x2, x1, x1^2 ] [ x1*x3, x2, x1^2 ] [ x2*x3, x1, x1^2 ] [ x1*x3, x1^3*x2, x1^2 ] [ x3, x2, x1^2 ] [ x3, x1, x1^2 ] [ x3, x1^3*x2, x1^2 ] [ x2, x1, x1^2 ] [ x1*x3, x2, x1^2 ] [ x2*x3, x1, x1^2 ] [ x1*x3, x1^3*x2, x1^2 ] [ x3*x4, x3, x2, x2^2 ] [ x3*x4, x3, x1, x2^2 ] [ x3*x4, x3, x1*x2, x2^2 ] [ x3*x4, x2, x1, x2^2 ] [ x3*x4, x1*x3, x2, x2^2 ] [ x3*x4, x2*x3, x1, x2^2 ] [ x3*x4, x1*x3, x1*x2, x2^2 ] [ x3, x2, x1, x2^2 ] [ x1*x3*x4, x3, x2, x2^2 ] [ x2*x3*x4, x3, x1, x2^2 ] [ x1*x3*x4, x3, x1*x2, x2^2 ] [ x4, x2, x1, x2^2 ] [ x1*x3*x4, x1*x3, x2, x2^2 ] [ x2*x3*x4, x2*x3, x1, x2^2 ] [ x1*x3*x4, x1*x3, x1*x2, x2^2 ] [ x1*x2*x1*x2*x3*x4, x3, x2, x1*x2*x1*x2 ] [ x1*x2*x1*x2*x3*x4, x3, x2*x1*x2, x1*x2*x1*x2 ] [ x1*x2*x1*x2*x3*x4, x3, x1*x2, x1*x2*x1*x2 ] [ x1*x2*x1*x2*x3*x4, x2, x2*x1*x2, x1*x2*x1*x2 ] [ x1*x2*x1*x2*x3*x4, x2*x1*x2*x3, x2, x1*x2*x1*x2 ] [ x1*x2*x1*x2*x3*x4, x2*x3, x2*x1*x2, x1*x2*x1*x2 ] [ x1*x2*x1*x2*x3*x4, x2*x1*x2*x3, x1*x2, x1*x2*x1*x2 ] [ x3, x2, x2*x1*x2, x1*x2*x1*x2 ] [ x1*x3*x4, x3, x2, x1*x2*x1*x2 ] [ x1*x2*x1*x3*x4, x3, x2*x1*x2, x1*x2*x1*x2 ] [ x1*x3*x4, x3, x1*x2, x1*x2*x1*x2 ] [ x1*x2*x1*x2*x4, x2, x2*x1*x2, x1*x2*x1*x2 ] [ x1*x3*x4, x2*x1*x2*x3, x2, x1*x2*x1*x2 ] [ x1*x2*x1*x3*x4, x2*x3, x2*x1*x2, x1*x2*x1*x2 ] [ x1*x3*x4, x2*x1*x2*x3, x1*x2, x1*x2*x1*x2 ] [ x4, x1, x2, x1*x4*x1*x4 ] [ x4, x1, x2*x3, x1*x4*x1*x4 ] [ x4, x1, x3, x1*x4*x1*x4 ] [ x4, x2, x2*x3, x1*x4*x1*x4 ] [ x4, x1*x2*x3, x2, x1*x4*x1*x4 ] [ x4, x1*x2, x2*x3, x1*x4*x1*x4 ] [ x4, x1*x2*x3, x3, x1*x4*x1*x4 ] [ x1, x2, x2*x3, x1*x4*x1*x4 ] [ x2*x3*x4, x1, x2, x1*x4*x1*x4 ] [ x2*x4, x1, x2*x3, x1*x4*x1*x4 ] [ x2*x3*x4, x1, x3, x1*x4*x1*x4 ] [ x4*x1, x2, x2*x3, x1*x4*x1*x4 ] [ x2*x3*x4, x1*x2*x3, x2, x1*x4*x1*x4 ] [ x2*x4, x1*x2, x2*x3, x1*x4*x1*x4 ] [ x2*x3*x4, x1*x2*x3, x3, x1*x4*x1*x4 ] [ 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 ] [ 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, x3, x1, x2*x3*x2*x3 ] [ x4, x3, x1*x2, x2*x3*x2*x3 ] [ x4, x3, x2, x2*x3*x2*x3 ] [ x4, x1, x1*x2, x2*x3*x2*x3 ] [ x4, x1*x3*x2, x1, x2*x3*x2*x3 ] [ x4, x1*x3, x1*x2, x2*x3*x2*x3 ] [ x4, x1*x3*x2, x2, x2*x3*x2*x3 ] [ x3, x1, x1*x2, x2*x3*x2*x3 ] [ x1*x2*x4, x3, x1, x2*x3*x2*x3 ] [ x1*x4, x3, x1*x2, x2*x3*x2*x3 ] [ x1*x2*x4, x3, x2, x2*x3*x2*x3 ] [ x3*x4, x1, x1*x2, x2*x3*x2*x3 ] [ x1*x2*x4, x1*x3*x2, x1, x2*x3*x2*x3 ] [ x1*x4, x1*x3, x1*x2, x2*x3*x2*x3 ] [ x1*x2*x4, x1*x3*x2, x2, 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 ] [ 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 ] [ x2*x4, x3, x3*x1*x3, x1*x3*x1*x3 ] [ x2*x4, x3, x2, x1*x3*x1*x3 ] [ x2*x4, x3, x2*x3*x1*x3, x1*x3*x1*x3 ] [ x2*x4, x3*x1*x3, x2, x1*x3*x1*x3 ] [ x2*x4, x2*x3, x3*x1*x3, x1*x3*x1*x3 ] [ x2*x4, x1*x3, x2, x1*x3*x1*x3 ] [ x2*x4, x2*x3, x2*x3*x1*x3, x1*x3*x1*x3 ] [ x3, x3*x1*x3, x2, x1*x3*x1*x3 ] [ x4, x3, x3*x1*x3, x1*x3*x1*x3 ] [ x2*x3*x1*x3*x4, x3, x2, x1*x3*x1*x3 ] [ x4, x3, x2*x3*x1*x3, x1*x3*x1*x3 ] [ x2*x3*x4, x3*x1*x3, x2, x1*x3*x1*x3 ] [ x4, x2*x3, x3*x1*x3, x1*x3*x1*x3 ] [ x2*x3*x1*x3*x4, x1*x3, x2, x1*x3*x1*x3 ] [ x4, x2*x3, x2*x3*x1*x3, x1*x3*x1*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 ] [ 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, x1, x2, x2*x4*x2*x4 ] [ x4, x1, x3, x2*x4*x2*x4 ] [ x4, x1, x2*x3, x2*x4*x2*x4 ] [ x4, x2, x3, x2*x4*x2*x4 ] [ x4, x1*x3, x2, x2*x4*x2*x4 ] [ x4, x1*x2, x3, x2*x4*x2*x4 ] [ x4, x1*x3, x2*x3, x2*x4*x2*x4 ] [ x1, x2, x3, x2*x4*x2*x4 ] [ x3*x4, x1, x2, x2*x4*x2*x4 ] [ x4*x2, x1, x3, x2*x4*x2*x4 ] [ x3*x4, x1, x2*x3, x2*x4*x2*x4 ] [ x1*x4, x2, x3, x2*x4*x2*x4 ] [ x3*x4, x1*x3, x2, x2*x4*x2*x4 ] [ x4*x2, x1*x2, x3, x2*x4*x2*x4 ] [ x3*x4, x1*x3, x2*x3, x2*x4*x2*x4 ] [ 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, x3^2 ] [ x4, x3, x2, x3^2 ] [ x4, x3, x1*x2, x3^2 ] [ x4, x1, x2, x3^2 ] [ x4, x2*x3, x1, x3^2 ] [ x4, x3*x1, x2, x3^2 ] [ x4, x2*x3, x1*x2, x3^2 ] [ x3, x1, x2, x3^2 ] [ x2*x4, x3, x1, x3^2 ] [ x1*x4, x3, x2, x3^2 ] [ x2*x4, x3, x1*x2, x3^2 ] [ x3*x4, x1, x2, x3^2 ] [ x2*x4, x2*x3, x1, x3^2 ] [ x1*x4, x3*x1, x2, x3^2 ] [ x2*x4, x2*x3, x1*x2, x3^2 ] [ x3*x5, x4, x4*x1*x4, x2, x1*x4*x1*x4 ] [ x3*x5, x4, x4*x1*x4, x3, x1*x4*x1*x4 ] [ x3*x5, x4, x4*x1*x4, x2*x3, x1*x4*x1*x4 ] [ x3*x5, x4, x2, x3, x1*x4*x1*x4 ] [ x3*x5, x4, x3*x4*x1*x4, x2, x1*x4*x1*x4 ] [ x3*x5, x4, x2*x4*x1*x4, x3, x1*x4*x1*x4 ] [ x3*x5, x4, x3*x4*x1*x4, x2*x3, x1*x4*x1*x4 ] [ x3*x5, x4*x1*x4, x2, x3, x1*x4*x1*x4 ] [ x3*x5, x3*x4, x4*x1*x4, x2, x1*x4*x1*x4 ] [ x3*x5, x2*x4, x4*x1*x4, x3, x1*x4*x1*x4 ] [ x3*x5, x3*x4, x4*x1*x4, x2*x3, x1*x4*x1*x4 ] [ x3*x5, x1*x4, x2, x3, x1*x4*x1*x4 ] [ x3*x5, x3*x4, x3*x4*x1*x4, x2, x1*x4*x1*x4 ] [ x3*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 ] [ x4, x4*x1*x4, x2, x3, x1*x4*x1*x4 ] [ x5, x4, x4*x1*x4, x2, x1*x4*x1*x4 ] [ x2*x3*x5, x4, x4*x1*x4, x3, x1*x4*x1*x4 ] [ x5, x4, x4*x1*x4, x2*x3, x1*x4*x1*x4 ] [ x3*x4*x1*x4*x5, x4, x2, x3, x1*x4*x1*x4 ] [ x5, x4, x3*x4*x1*x4, x2, x1*x4*x1*x4 ] [ x2*x3*x5, x4, x2*x4*x1*x4, x3, x1*x4*x1*x4 ] [ x5, x4, x3*x4*x1*x4, x2*x3, x1*x4*x1*x4 ] [ x3*x4*x5, x4*x1*x4, x2, x3, x1*x4*x1*x4 ] [ x5, x3*x4, x4*x1*x4, x2, x1*x4*x1*x4 ] [ x2*x3*x5, x2*x4, x4*x1*x4, x3, x1*x4*x1*x4 ] [ x5, x3*x4, x4*x1*x4, x2*x3, x1*x4*x1*x4 ] [ x3*x4*x1*x4*x5, x1*x4, x2, x3, x1*x4*x1*x4 ] [ x5, x3*x4, x3*x4*x1*x4, x2, x1*x4*x1*x4 ] [ x2*x3*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 ] [ x1*x2, x2^2 ] [ x1, x2^2 ] [ x2, x2^2 ] [ x1^2*x2, x1^2 ] [ x1, x1^2 ] [ x1^3*x2, x1^2 ] [ x1^2*x2, x1^2 ] [ x1, x1^2 ] [ x1^3*x2, x1^2 ] [ x2, x1^2 ] [ x1, x1^2 ] [ x1*x2, x1^2 ] [ x1^2*x2, x1^2 ] [ x1, x1^2 ] [ x1^3*x2, x1^2 ] [ x1*x2, x2^2 ] [ x1, x2^2 ] [ x2, x2^2 ] [ 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 ] [ x2, x1*x2*x1*x2 ] [ x1, x1*x2*x1*x2 ] [ x2*x1, x1*x2*x1*x2 ] [ x2, x1*x2*x1*x2 ] [ x1, x1*x2*x1*x2 ] [ x2*x1, x1*x2*x1*x2 ] [ x1*x2*x1, x1*x2*x1*x2 ] [ x2*x1*x2, x1*x2*x1*x2 ] [ x2*x1, x1*x2*x1*x2 ] [ x2, x1*x2*x1*x2 ] [ x2*x1*x2, x1*x2*x1*x2 ] [ x1*x2, x1*x2*x1*x2 ] [ x2, x1*x2*x1*x2 ] [ x1, x1*x2*x1*x2 ] [ x2*x1, x1*x2*x1*x2 ] [ x2, x2^2 ] [ x1, x2^2 ] [ x2*x1, x2^2 ] gap> LogTo();