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)^2(8)^2/group.1126");
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> P1 := Group(R.generators);
<matrix group with 3 generators>
gap> Append(names,["ordnung.16/(2)^2(8)^2/words.group.1126"]);
gap> Append(GROUPS,[P1]);
gap> R := CaratReadBravaisFile("ordnung.16/(2)^4(16)^2/group.1127");
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> P2 := Group(R.generators);
<matrix group with 3 generators>
gap> Append(names,["ordnung.16/(2)^4(16)^2/words.group.1127"]);
gap> Append(GROUPS,[P2]);
gap> R := CaratReadBravaisFile("ordnung.16/(2)^4(16)^2/group.1128");
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> P3 := Group(R.generators);
<matrix group with 3 generators>
gap> Append(names,["ordnung.16/(2)^4(16)^2/words.group.1128"]);
gap> Append(GROUPS,[P3]);
gap> R := CaratReadBravaisFile("ordnung.16/(2)^4(8)^2/group.1129");
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)^4(8)^2/words.group.1129"]);
gap> Append(GROUPS,[P4]);
gap> R := CaratReadBravaisFile("ordnung.16/(2)^4(8)^2/group.1130");
rec(
generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1,
0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ]
, [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ]
] ], size := 16 )
gap> P5 := Group(R.generators);
<matrix group with 3 generators>
gap> Append(names,["ordnung.16/(2)^4(8)^2/words.group.1130"]);
gap> Append(GROUPS,[P5]);
gap> R := CaratReadBravaisFile("ordnung.16/(2)^4(8)^2/group.1131");
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)^4(8)^2/words.group.1131"]);
gap> Append(GROUPS,[P6]);
gap> R := CaratReadBravaisFile("ordnung.32/(2)^4(8)^2/group.1132");
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> P7 := Group(R.generators);
<matrix group with 4 generators>
gap> Append(names,["ordnung.32/(2)^4(8)^2/words.group.1132"]);
gap> Append(GROUPS,[P7]);
gap> R := CaratReadBravaisFile("ordnung.4/(2)^2(16)^2/min.225");
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 ] ] ], size := 4 )
gap> P8 := Group(R.generators);
<matrix group with 1 generators>
gap> Append(names,["ordnung.4/(2)^2(16)^2/words.min.225"]);
gap> Append(GROUPS,[P8]);
gap> R := CaratReadBravaisFile("ordnung.8/(2)^2(16)^2/group.1133");
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> P9 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.8/(2)^2(16)^2/words.group.1133"]);
gap> Append(GROUPS,[P9]);
gap> R := CaratReadBravaisFile("ordnung.8/(2)^2(8)^2/group.1134");
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> P10 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.8/(2)^2(8)^2/words.group.1134"]);
gap> Append(GROUPS,[P10]);
gap> R := CaratReadBravaisFile("ordnung.8/(2)^2(8)^2/group.1135");
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> P11 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.8/(2)^2(8)^2/words.group.1135"]);
gap> Append(GROUPS,[P11]);
gap> R := CaratReadBravaisFile("ordnung.8/(2)^4(16)^2/group.1136");
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> P12 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.8/(2)^4(16)^2/words.group.1136"]);
gap> Append(GROUPS,[P12]);
gap> R := CaratReadBravaisFile("ordnung.8/(2)^4(16)^2/group.1137");
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> P13 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.8/(2)^4(16)^2/words.group.1137"]);
gap> Append(GROUPS,[P13]);
gap> R := CaratReadBravaisFile("ordnung.8/(2)^4(16)^2/min.226");
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> P14 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.8/(2)^4(16)^2/words.min.226"]);
gap> Append(GROUPS,[P14]);
gap> R := CaratReadBravaisFile("ordnung.8/(2)^4(16)^2/min.227");
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> P15 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.8/(2)^4(16)^2/words.min.227"]);
gap> Append(GROUPS,[P15]);
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 ] ],
[ [ 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 ] ]
,
[ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ]
],
[ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ]
] ]),
Group([ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ],
[ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ]
] ]),
Group([ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ]
, [ [ 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 ] ],
[ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 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 ]
] ]),
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 ]
] ]),
Group([ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ],
[ [ 0, -1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ]
] ]),
Group([ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ],
[ [ 0, -1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ]
]),
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 ]
] ]),
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 ] ]
]),
Group([ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ]
, [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1 ] ],
[ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ]
] ]),
Group([ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ]
, [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1 ] ],
[ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ]
]) ]
gap> Print(names,"\n");
[ "ordnung.16/(2)^2(8)^2/words.group.1126",
"ordnung.16/(2)^4(16)^2/words.group.1127",
"ordnung.16/(2)^4(16)^2/words.group.1128",
"ordnung.16/(2)^4(8)^2/words.group.1129",
"ordnung.16/(2)^4(8)^2/words.group.1130",
"ordnung.16/(2)^4(8)^2/words.group.1131",
"ordnung.32/(2)^4(8)^2/words.group.1132",
"ordnung.4/(2)^2(16)^2/words.min.225",
"ordnung.8/(2)^2(16)^2/words.group.1133",
"ordnung.8/(2)^2(8)^2/words.group.1134",
"ordnung.8/(2)^2(8)^2/words.group.1135",
"ordnung.8/(2)^4(16)^2/words.group.1136",
"ordnung.8/(2)^4(16)^2/words.group.1137",
"ordnung.8/(2)^4(16)^2/words.min.226",
"ordnung.8/(2)^4(16)^2/words.min.227" ]
gap> Size(GROUPS);
15
gap> Size(names);
15
gap> Read("../../TGROUPS.GAP");
gap> for i in [1..Size(GROUPS)] do
> SubgroupWords(GROUPS[i], names[i]);
> od;
[ 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, x1, x2*x3*x2*x3 ]
[ x2*x3*x2, x3*x2*x3, x2*x3*x2*x3 ]
[ x2*x3*x2, x1*x3*x2*x3, x2*x3*x2*x3 ]
[ x1, x3*x2*x3, x2*x3*x2*x3 ]
[ x3*x2, x1, x2*x3*x2*x3 ]
[ x1*x2*x3*x2, x3*x2*x3, x2*x3*x2*x3 ]
[ x3*x2, x1*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 ]
[ 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, 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, x3*x1*x3, x1*x3*x1*x3 ]
[ x3, x2, x1*x3*x1*x3 ]
[ x3, x2*x3*x1*x3, x1*x3*x1*x3 ]
[ x3*x1*x3, x2, x1*x3*x1*x3 ]
[ x2*x3, x3*x1*x3, x1*x3*x1*x3 ]
[ x1*x3, x2, x1*x3*x1*x3 ]
[ x2*x3, x2*x3*x1*x3, x1*x3*x1*x3 ]
[ x4, x3, x3*x1*x3, x1*x3*x1*x3 ]
[ x4, x3, x2, x1*x3*x1*x3 ]
[ x4, x3, x2*x3*x1*x3, x1*x3*x1*x3 ]
[ x4, x3*x1*x3, x2, x1*x3*x1*x3 ]
[ x4, x2*x3, x3*x1*x3, x1*x3*x1*x3 ]
[ x4, x1*x3, x2, x1*x3*x1*x3 ]
[ x4, x2*x3, x2*x3*x1*x3, x1*x3*x1*x3 ]
[ x3, x3*x1*x3, x2, x1*x3*x1*x3 ]
[ x2*x4, x3, x3*x1*x3, x1*x3*x1*x3 ]
[ x3*x1*x3*x4, x3, x2, x1*x3*x1*x3 ]
[ x2*x4, x3, x2*x3*x1*x3, x1*x3*x1*x3 ]
[ x3*x4, x3*x1*x3, x2, x1*x3*x1*x3 ]
[ x2*x4, x2*x3, x3*x1*x3, x1*x3*x1*x3 ]
[ x3*x1*x3*x4, x1*x3, x2, x1*x3*x1*x3 ]
[ x2*x4, x2*x3, x2*x3*x1*x3, x1*x3*x1*x3 ]
[ x1^2 ]
[ x1^2*x2, x1^2 ]
[ x1, x1^2 ]
[ x1^3*x2, x1^2 ]
[ x2, x2^2 ]
[ x1, x2^2 ]
[ x1*x2, x2^2 ]
[ x2, x2^2 ]
[ x1, x2^2 ]
[ x1*x2, x2^2 ]
[ x2, x1*x2*x1*x2 ]
[ x2*x1*x2, x1*x2*x1*x2 ]
[ x1*x2, 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 ]
[ 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 ]
gap> LogTo();