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.24/(1)^2(4)^3(12)^1/min.352");
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, -1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, -1 ], [ 0, 0, 1, 0, -1, 0 ]
] ], size := 24 )
gap> P1 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.24/(1)^2(4)^3(12)^1/words.min.352"]);
gap> Append(GROUPS,[P1]);
gap> R := CaratReadBravaisFile("ordnung.24/(1)^2(4)^3(12)^1/min.353");
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, 1, 0, -1 ],
[ 0, 0, 1, 0, -1, 0 ] ],
[ [ 0, -1, 0, 0, 0, 0 ], [ 1, -1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ],
[ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, -1 ], [ 0, 0, -1, 0, 1, 0 ]
] ], size := 24 )
gap> P2 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.24/(1)^2(4)^3(12)^1/words.min.353"]);
gap> Append(GROUPS,[P2]);
gap> R := CaratReadBravaisFile("ordnung.24/(1)^2(4)^3(12)^1/min.354");
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, -1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, -1 ], [ 0, 0, 1, 0, -1, 0 ]
] ], size := 24 )
gap> P3 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.24/(1)^2(4)^3(12)^1/words.min.354"]);
gap> Append(GROUPS,[P3]);
gap> R := CaratReadBravaisFile("ordnung.24/(1)^4(4)^2(12)^2/min.355");
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, 1, 0, -1 ],
[ 0, 0, 1, 0, -1, 0 ] ],
[ [ 1, -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 := 24 )
gap> P4 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.24/(1)^4(4)^2(12)^2/words.min.355"]);
gap> Append(GROUPS,[P4]);
gap> R := CaratReadBravaisFile("ordnung.24/(1)^4(4)^2(12)^2/min.356");
rec(
generators := [ [ [ -1, 0, 0, 0, 0, 0 ], [ -1, 1, 0, 0, 0, 0 ], [ 0, 0, 0,
1, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, -1 ],
[ 0, 0, 1, 0, -1, 0 ] ],
[ [ -1, 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 := 24 )
gap> P5 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.24/(1)^4(4)^2(12)^2/words.min.356"]);
gap> Append(GROUPS,[P5]);
gap> R := CaratReadBravaisFile("ordnung.24/(1)^4(4)^2(12)^2/min.357");
rec(
generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 1, -1, 0, 0, 0, 0 ], [ 0, 0, -1,
0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ],
[ 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, -1, 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, 1, 0, -1 ], [ 0, 0, 1, 0, -1, 0 ]
] ], size := 24 )
gap> P6 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.24/(1)^4(4)^2(12)^2/words.min.357"]);
gap> Append(GROUPS,[P6]);
gap> R := CaratReadBravaisFile("ordnung.24/(1)^4(4)^2(12)^2/min.358");
rec(
generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 1, -1, 0, 0, 0, 0 ], [ 0, 0, -1,
0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ],
[ 0, 0, 0, 0, 0, 1 ] ],
[ [ -1, 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, 1, 0, -1 ], [ 0, 0, -1, 0, 1, 0 ]
] ], size := 24 )
gap> P7 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.24/(1)^4(4)^2(12)^2/words.min.358"]);
gap> Append(GROUPS,[P7]);
gap> R := CaratReadBravaisFile("ordnung.48/(1)^2(4)^3(12)^1/group.1908");
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, -1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, -1 ], [ 0, 0, 1, 0, -1, 0 ]
] ], size := 48 )
gap> P8 := Group(R.generators);
<matrix group with 3 generators>
gap> Append(names,["ordnung.48/(1)^2(4)^3(12)^1/words.group.1908"]);
gap> Append(GROUPS,[P8]);
gap> R := CaratReadBravaisFile("ordnung.48/(1)^4(4)^2(12)^2/group.1909");
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, 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, 1, 0, -1 ], [ 0, 0, 1, 0, -1, 0 ]
] ], size := 48 )
gap> P9 := Group(R.generators);
<matrix group with 3 generators>
gap> Append(names,["ordnung.48/(1)^4(4)^2(12)^2/words.group.1909"]);
gap> Append(GROUPS,[P9]);
gap> R := CaratReadBravaisFile("ordnung.48/(1)^4(4)^2(12)^2/group.1910");
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, 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, -1, 0, 1 ], [ 0, 0, 1, 0, -1, 0 ]
] ], size := 48 )
gap> P10 := Group(R.generators);
<matrix group with 3 generators>
gap> Append(names,["ordnung.48/(1)^4(4)^2(12)^2/words.group.1910"]);
gap> Append(GROUPS,[P10]);
gap> R := CaratReadBravaisFile("ordnung.48/(1)^4(4)^2(12)^2/group.1911");
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, 1, 0, -1 ],
[ 0, 0, 1, 0, -1, 0 ] ],
[ [ -1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ]
,
[ [ -1, 0, 0, 0, 0, 0 ], [ -1, 1, 0, 0, 0, 0 ], [ 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 := 48 )
gap> P11 := Group(R.generators);
<matrix group with 3 generators>
gap> Append(names,["ordnung.48/(1)^4(4)^2(12)^2/words.group.1911"]);
gap> Append(GROUPS,[P11]);
gap> R := CaratReadBravaisFile("ordnung.48/(1)^4(4)^2(12)^2/group.1912");
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, -1, 0, 1 ],
[ 0, 0, 1, 0, -1, 0 ] ],
[ [ -1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ]
,
[ [ -1, 0, 0, 0, 0, 0 ], [ -1, 1, 0, 0, 0, 0 ], [ 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 := 48 )
gap> P12 := Group(R.generators);
<matrix group with 3 generators>
gap> Append(names,["ordnung.48/(1)^4(4)^2(12)^2/words.group.1912"]);
gap> Append(GROUPS,[P12]);
gap> R := CaratReadBravaisFile("ordnung.48/(1)^4(4)^2(12)^2/group.1913");
rec(
generators := [ [ [ -1, 0, 0, 0, 0, 0 ], [ -1, 1, 0, 0, 0, 0 ], [ 0, 0, 0,
1, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, -1 ],
[ 0, 0, 1, 0, -1, 0 ] ],
[ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ]
,
[ [ 1, -1, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 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 := 48 )
gap> P13 := Group(R.generators);
<matrix group with 3 generators>
gap> Append(names,["ordnung.48/(1)^4(4)^2(12)^2/words.group.1913"]);
gap> Append(GROUPS,[P13]);
gap> R := CaratReadBravaisFile("ordnung.96/(1)^4(4)^2(12)^2/group.1914");
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, 0, -1 ], [ 0, 0, 0, 0, -1, 0 ]
],
[ [ -1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ],
[ [ -1, 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 := 96 )
gap> P14 := Group(R.generators);
<matrix group with 4 generators>
gap> Append(names,["ordnung.96/(1)^4(4)^2(12)^2/words.group.1914"]);
gap> Append(GROUPS,[P14]);
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, -1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, -1 ], [ 0, 0, 1, 0, -1, 0 ]
] ]),
Group([ [ [ -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, 1, 0, -1 ],
[ 0, 0, 1, 0, -1, 0 ] ],
[ [ 0, -1, 0, 0, 0, 0 ], [ 1, -1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ],
[ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, -1 ], [ 0, 0, -1, 0, 1, 0 ]
] ]),
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, -1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, -1 ], [ 0, 0, 1, 0, -1, 0 ]
] ]),
Group([ [ [ 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, 1, 0, -1 ], [ 0, 0, 1, 0, -1, 0 ] ]
,
[ [ 1, -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 ], [ -1, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ]
, [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, -1 ],
[ 0, 0, 1, 0, -1, 0 ] ],
[ [ -1, 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 ], [ 1, -1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ]
, [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ],
[ 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, -1, 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, 1, 0, -1 ], [ 0, 0, 1, 0, -1, 0 ]
] ]),
Group([ [ [ 1, 0, 0, 0, 0, 0 ], [ 1, -1, 0, 0, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ]
, [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ],
[ 0, 0, 0, 0, 0, 1 ] ],
[ [ -1, 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, 1, 0, -1 ], [ 0, 0, -1, 0, 1, 0 ]
] ]),
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, -1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, -1 ], [ 0, 0, 1, 0, -1, 0 ]
] ]),
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, 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, 1, 0, -1 ], [ 0, 0, 1, 0, -1, 0 ]
] ]),
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, 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, -1, 0, 1 ], [ 0, 0, 1, 0, -1, 0 ]
] ]),
Group([ [ [ 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, 1, 0, -1 ], [ 0, 0, 1, 0, -1, 0 ] ]
,
[ [ -1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ]
,
[ [ -1, 0, 0, 0, 0, 0 ], [ -1, 1, 0, 0, 0, 0 ], [ 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, 0, -1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 1 ], [ 0, 0, 1, 0, -1, 0 ] ]
,
[ [ -1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ]
,
[ [ -1, 0, 0, 0, 0, 0 ], [ -1, 1, 0, 0, 0, 0 ], [ 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 ], [ -1, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ]
, [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, -1 ],
[ 0, 0, 1, 0, -1, 0 ] ],
[ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ]
,
[ [ 1, -1, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 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, 0, -1 ], [ 0, 0, 0, 0, -1, 0 ]
],
[ [ -1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ],
[ [ -1, 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.24/(1)^2(4)^3(12)^1/words.min.352",
"ordnung.24/(1)^2(4)^3(12)^1/words.min.353",
"ordnung.24/(1)^2(4)^3(12)^1/words.min.354",
"ordnung.24/(1)^4(4)^2(12)^2/words.min.355",
"ordnung.24/(1)^4(4)^2(12)^2/words.min.356",
"ordnung.24/(1)^4(4)^2(12)^2/words.min.357",
"ordnung.24/(1)^4(4)^2(12)^2/words.min.358",
"ordnung.48/(1)^2(4)^3(12)^1/words.group.1908",
"ordnung.48/(1)^4(4)^2(12)^2/words.group.1909",
"ordnung.48/(1)^4(4)^2(12)^2/words.group.1910",
"ordnung.48/(1)^4(4)^2(12)^2/words.group.1911",
"ordnung.48/(1)^4(4)^2(12)^2/words.group.1912",
"ordnung.48/(1)^4(4)^2(12)^2/words.group.1913",
"ordnung.96/(1)^4(4)^2(12)^2/words.group.1914" ]
gap> Size(GROUPS);
14
gap> Size(names);
14
gap> Read("../../TGROUPS.GAP");
gap> for i in [1..Size(GROUPS)] do
> SubgroupWords(GROUPS[i], names[i]);
> od;
[ x2^3, x2^2, x1*x2*x1*x2^5 ]
[ x1, x2^2, x1*x2*x1*x2^5 ]
[ x2*x1*x2^2, x2^2, x1*x2*x1*x2^5 ]
[ x2^3, x1, x1*x2*x1*x2^5 ]
[ x1*x2^3, x1*x2*x1*x2, x2^6 ]
[ x1, x1*x2*x1*x2, x2^6 ]
[ x1*x2*x1*x2^2, x1*x2*x1*x2, x2^6 ]
[ x1*x2^3, x1, x2^6 ]
[ x2^3, x2^2, x1*x2*x1*x2^5 ]
[ x1, x2^2, x1*x2*x1*x2^5 ]
[ x2*x1*x2^2, x2^2, x1*x2*x1*x2^5 ]
[ x2^3, x1, x1*x2*x1*x2^5 ]
[ x2^3*x1, x1*x2*x1*x2, x2^2 ]
[ x1, x1*x2*x1*x2, x2^2 ]
[ x2^3, x1*x2*x1*x2, x2^2 ]
[ x2^3*x1, x1, x1*x2*x1*x2 ]
[ x2^3, x1*x2*x1*x2, x2^2 ]
[ x1, x1*x2*x1*x2, x2^2 ]
[ x2^3*x1, x1*x2*x1*x2, x2^2 ]
[ x2^3, x1, x1*x2*x1*x2 ]
[ x1*x2*x1*x2*x1*x2*x1, x1*x2*x1*x2*x1*x2*x1*x2*x1*x2*x1*x2,
x2*x1*x2*x1*x2*x1*x2*x1 ]
[ x2*x1*x2*x1*x2*x1*x2*x1*x2*x1*x2, x1*x2*x1*x2*x1*x2*x1*x2*x1*x2*x1*x2,
x2*x1*x2*x1*x2*x1*x2*x1 ]
[ x2*x1*x2*x1*x2*x1, x1*x2*x1*x2*x1*x2*x1*x2*x1*x2*x1*x2,
x2*x1*x2*x1*x2*x1*x2*x1 ]
[ x1*x2*x1*x2*x1*x2*x1, x2*x1*x2*x1*x2*x1*x2*x1*x2*x1*x2,
x1*x2*x1*x2*x1*x2*x1*x2*x1*x2*x1*x2 ]
[ x1*x2^3*x1, x2^6, x1*x2^4*x1 ]
[ x1*x2^2, x2^6, x1*x2^4*x1 ]
[ x1*x2^5, x2^6, x1*x2^4*x1 ]
[ x1*x2^3*x1, x1*x2^2, x2^6 ]
[ x3^3, x1, x3^2, x1*x3*x1*x3^5 ]
[ x3^3, x2, x3^2, x1*x3*x1*x3^5 ]
[ x3^3, x1*x2, x3^2, x1*x3*x1*x3^5 ]
[ x1, x2, x3^2, x1*x3*x1*x3^5 ]
[ x2*x3^3, x1, x3^2, x1*x3*x1*x3^5 ]
[ x3*x1*x3^2, x2, x3^2, x1*x3*x1*x3^5 ]
[ x2*x3^3, x1*x2, x3^2, x1*x3*x1*x3^5 ]
[ x3^3, x1, x2, x1*x3*x1*x3^5 ]
[ x3^3, x3^2*x1, x1*x3*x1*x3, x3^2 ]
[ x3^3, x2*x3^2*x1, x1*x3*x1*x3, x3^2 ]
[ x3^3, x2, x1*x3*x1*x3, x3^2 ]
[ x3^2*x1, x2*x3^2*x1, x1*x3*x1*x3, x3^2 ]
[ x2*x3*x1*x3^2, x3^2*x1, x1*x3*x1*x3, x3^2 ]
[ x3*x1*x3^2, x2*x3^2*x1, x1*x3*x1*x3, x3^2 ]
[ x2*x3*x1*x3^2, x2, x1*x3*x1*x3, x3^2 ]
[ x3^3, x3^2*x1, x2*x3^2*x1, x1*x3*x1*x3 ]
[ x1*x3^3*x1, x1*x3^4, x3^6, x1*x3^4*x1 ]
[ x1*x3^3*x1, x1*x2*x3^4, x3^6, x1*x3^4*x1 ]
[ x1*x3^3*x1, x2, x3^6, x1*x3^4*x1 ]
[ x1*x3^4, x1*x2*x3^4, x3^6, x1*x3^4*x1 ]
[ x2*x3^5*x1, x1*x3^4, x3^6, x1*x3^4*x1 ]
[ x3^5*x1, x1*x2*x3^4, x3^6, x1*x3^4*x1 ]
[ x2*x3^5*x1, x2, x3^6, x1*x3^4*x1 ]
[ x1*x3^3*x1, x1*x3^4, x1*x2*x3^4, x3^6 ]
[ x2*x3*x1*x3*x1*x3, x2*x1, x1*x2*x1*x2, x1*x3*x1*x3 ]
[ x2*x3*x1*x3*x1*x3, x1, x1*x2*x1*x2, x1*x3*x1*x3 ]
[ x2*x3*x1*x3*x1*x3, x2, x1*x2*x1*x2, x1*x3*x1*x3 ]
[ x2*x1, x1, x1*x2*x1*x2, x1*x3*x1*x3 ]
[ x2*x1*x3*x1*x3*x1*x3, x2*x1, x1*x2*x1*x2, x1*x3*x1*x3 ]
[ x1*x3*x1*x3*x1*x3, x1, x1*x2*x1*x2, x1*x3*x1*x3 ]
[ x2*x1*x3*x1*x3*x1*x3, x2, x1*x2*x1*x2, x1*x3*x1*x3 ]
[ x2*x3*x1*x3*x1*x3, x2*x1, x1, x1*x2*x1*x2 ]
[ x1^2*x2*x3*x1*x3*x1*x3, x1^3*x2, x1^2, x1^3*x3*x1*x3 ]
[ x1^2*x2*x3*x1*x3*x1*x3, x1, x1^2, x1^3*x3*x1*x3 ]
[ x1^2*x2*x3*x1*x3*x1*x3, x1^2*x2, x1^2, x1^3*x3*x1*x3 ]
[ x1^3*x2, x1, x1^2, x1^3*x3*x1*x3 ]
[ x1*x2*x3*x1*x3*x1*x3, x1^3*x2, x1^2, x1^3*x3*x1*x3 ]
[ x1^3*x3*x1*x3*x1*x3, x1, x1^2, x1^3*x3*x1*x3 ]
[ x1*x2*x3*x1*x3*x1*x3, x1^2*x2, x1^2, x1^3*x3*x1*x3 ]
[ x1^2*x2*x3*x1*x3*x1*x3, x1^3*x2, x1, x1^2 ]
[ x3*x1*x3*x1*x3, x2, x1*x2*x1*x2, x1*x3*x1*x3 ]
[ x3*x1*x3*x1*x3, x1, x1*x2*x1*x2, x1*x3*x1*x3 ]
[ x3*x1*x3*x1*x3, x2*x1, x1*x2*x1*x2, x1*x3*x1*x3 ]
[ x2, x1, x1*x2*x1*x2, x1*x3*x1*x3 ]
[ x1*x3*x1*x3*x1*x3, x2, x1*x2*x1*x2, x1*x3*x1*x3 ]
[ x2*x3*x1*x3*x1*x3, x1, x1*x2*x1*x2, x1*x3*x1*x3 ]
[ x1*x3*x1*x3*x1*x3, x2*x1, x1*x2*x1*x2, x1*x3*x1*x3 ]
[ x3*x1*x3*x1*x3, x2, x1, x1*x2*x1*x2 ]
[ x4^3, x4^2*x1, x2, x1*x2*x4*x1*x2*x4, x4^2 ]
[ x4^3, x4^2*x1, x3*x4^2*x1, x1*x2*x4*x1*x2*x4, x4^2 ]
[ x4^3, x4^2*x1, x2*x3*x4^2*x1, x1*x2*x4*x1*x2*x4, x4^2 ]
[ x4^3, x2, x3*x4^2*x1, x1*x2*x4*x1*x2*x4, x4^2 ]
[ x4^3, x3, x2, x1*x2*x4*x1*x2*x4, x4^2 ]
[ x4^3, x2*x4^2*x1, x3*x4^2*x1, x1*x2*x4*x1*x2*x4, x4^2 ]
[ x4^3, x3, x2*x3*x4^2*x1, x1*x2*x4*x1*x2*x4, x4^2 ]
[ x4^2*x1, x2, x3*x4^2*x1, x1*x2*x4*x1*x2*x4, x4^2 ]
[ x1*x3*x4, x4^2*x1, x2, x1*x2*x4*x1*x2*x4, x4^2 ]
[ x4*x2*x4^2, x4^2*x1, x3*x4^2*x1, x1*x2*x4*x1*x2*x4, x4^2 ]
[ x1*x3*x4, x4^2*x1, x2*x3*x4^2*x1, x1*x2*x4*x1*x2*x4, x4^2 ]
[ x1*x4, x2, x3*x4^2*x1, x1*x2*x4*x1*x2*x4, x4^2 ]
[ x1*x3*x4, x3, x2, x1*x2*x4*x1*x2*x4, x4^2 ]
[ x4*x2*x4^2, x2*x4^2*x1, x3*x4^2*x1, x1*x2*x4*x1*x2*x4, x4^2 ]
[ x1*x3*x4, x3, x2*x3*x4^2*x1, x1*x2*x4*x1*x2*x4, x4^2 ]
[ x4^3, x4^2*x1, x2, x3*x4^2*x1, x1*x2*x4*x1*x2*x4 ]
gap> LogTo();