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.12/(2)^2(6)^4/group.1641");
rec(
generators := [ [ [ 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, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1 ] ],
[ [ 0, -1, 0, 0, 0, 0 ], [ 1, -1, 0, 0, 0, 0 ], [ -1, 0, 0, -1, 0, 0 ],
[ -1, 1, 1, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ]
] ], size := 12 )
gap> P1 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.12/(2)^2(6)^4/words.group.1641"]);
gap> Append(GROUPS,[P1]);
gap> R := CaratReadBravaisFile("ordnung.12/(2)^2(6)^4/group.1642");
rec(
generators := [ [ [ -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, 0, -1, 0 ],
[ 0, 0, 0, 0, 0, 1 ] ],
[ [ -1, 1, 0, 0, 0, 0 ], [ -1, 0, 0, 0, 0, 0 ], [ 1, 0, -1, 1, 0, 0 ],
[ 1, -1, -1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ]
] ], size := 12 )
gap> P2 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.12/(2)^2(6)^4/words.group.1642"]);
gap> Append(GROUPS,[P2]);
gap> R := CaratReadBravaisFile("ordnung.12/(2)^2(6)^4/group.1643");
rec(
generators := [ [ [ -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, 0, -1, 0 ],
[ 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, -1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ -1, 0, 1, -1, 0, 0 ],
[ -1, 1, 1, 0, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ]
] ], size := 12 )
gap> P3 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.12/(2)^2(6)^4/words.group.1643"]);
gap> Append(GROUPS,[P3]);
gap> R := CaratReadBravaisFile("ordnung.12/(2)^2(6)^4/group.1644");
rec(
generators := [ [ [ -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, 0, -1, 0 ],
[ 0, 0, 0, 0, 0, -1 ] ],
[ [ 1, -1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ -1, 0, 1, -1, 0, 0 ],
[ -1, 1, 1, 0, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ]
] ], size := 12 )
gap> P4 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.12/(2)^2(6)^4/words.group.1644"]);
gap> Append(GROUPS,[P4]);
gap> R := CaratReadBravaisFile("ordnung.12/(2)^4(6)^2/group.1645");
rec(
generators := [ [ [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, -1, 0, 0 ], [ 1, 0, 0,
0, 0, 0 ], [ 1, -1, 0, 0, 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, -1, 1, 0, 0 ],
[ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ]
] ], size := 12 )
gap> P5 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.12/(2)^4(6)^2/words.group.1645"]);
gap> Append(GROUPS,[P5]);
gap> R := CaratReadBravaisFile("ordnung.12/(2)^4(6)^2/group.1646");
rec(
generators := [ [ [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, -1, 0, 0 ], [ 1, 0, 0,
0, 0, 0 ], [ 1, -1, 0, 0, 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, 1, -1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] ]
, size := 12 )
gap> P6 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.12/(2)^4(6)^2/words.group.1646"]);
gap> Append(GROUPS,[P6]);
gap> R := CaratReadBravaisFile("ordnung.12/(6)^6/group.1647");
rec(
generators := [ [ [ -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, 0, -1, 0 ],
[ 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, -1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ -1, 0, 1, -1, 0, 0 ],
[ -1, 1, 1, 0, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ]
] ], size := 12 )
gap> P7 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.12/(6)^6/words.group.1647"]);
gap> Append(GROUPS,[P7]);
gap> R := CaratReadBravaisFile("ordnung.24/(2)^2(6)^4/group.1648");
rec(
generators := [ [ [ 1, 1, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, -1,
1, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1 ] ],
[ [ -1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 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, -1, 1, 0, 0 ],
[ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ]
] ], size := 24 )
gap> P8 := Group(R.generators);
<matrix group with 3 generators>
gap> Append(names,["ordnung.24/(2)^2(6)^4/words.group.1648"]);
gap> Append(GROUPS,[P8]);
gap> R := CaratReadBravaisFile("ordnung.24/(2)^4(6)^2/group.1649");
rec(
generators := [ [ [ 0, 0, -1, 1, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, -1, 0,
0, 0, 0 ], [ 1, -1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, -1 ] ],
[ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ]
,
[ [ 0, -1, 0, 0, 0, 0 ], [ 1, -1, 0, 0, 0, 0 ], [ 0, 0, -1, 1, 0, 0 ],
[ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ]
] ], size := 24 )
gap> P9 := Group(R.generators);
<matrix group with 3 generators>
gap> Append(names,["ordnung.24/(2)^4(6)^2/words.group.1649"]);
gap> Append(GROUPS,[P9]);
gap> R := CaratReadBravaisFile("ordnung.24/(2)^4(6)^2/group.1650");
rec(
generators := [ [ [ 0, 0, -1, 1, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, -1, 0,
0, 0, 0 ], [ 1, -1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, -1 ] ],
[ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ]
,
[ [ 0, 1, 0, 0, 0, 0 ], [ -1, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ]
], size := 24 )
gap> P10 := Group(R.generators);
<matrix group with 3 generators>
gap> Append(names,["ordnung.24/(2)^4(6)^2/words.group.1650"]);
gap> Append(GROUPS,[P10]);
gap> R := CaratReadBravaisFile("ordnung.24/(2)^4(6)^2/group.1651");
rec(
generators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -1,
0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, -1 ] ],
[ [ -1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 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, -1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ]
] ], size := 24 )
gap> P11 := Group(R.generators);
<matrix group with 3 generators>
gap> Append(names,["ordnung.24/(2)^4(6)^2/words.group.1651"]);
gap> Append(GROUPS,[P11]);
gap> R := CaratReadBravaisFile("ordnung.24/(2)^4(6)^2/group.1652");
rec(
generators := [ [ [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, -1, 1, 0, 0 ], [ -1, 0, 0,
0, 0, 0 ], [ -1, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, -1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] ]
, size := 24 )
gap> P12 := Group(R.generators);
<matrix group with 3 generators>
gap> Append(names,["ordnung.24/(2)^4(6)^2/words.group.1652"]);
gap> Append(GROUPS,[P12]);
gap> R := CaratReadBravaisFile("ordnung.24/(2)^4(6)^2/group.1653");
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, 0, -1, 0, 0, 0 ], [ 0, 0, -1, 1, 0, 0 ], [ -1, 0, 0, 0, 0, 0 ],
[ -1, 1, 0, 0, 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, 1, -1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] ]
, size := 24 )
gap> P13 := Group(R.generators);
<matrix group with 3 generators>
gap> Append(names,["ordnung.24/(2)^4(6)^2/words.group.1653"]);
gap> Append(GROUPS,[P13]);
gap> R := CaratReadBravaisFile("ordnung.48/(2)^4(6)^2/group.1654");
rec(
generators := [ [ [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, -1, 1, 0, 0 ], [ -1, 0, 0,
0, 0, 0 ], [ -1, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ],
[ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ]
,
[ [ 1, -1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] ]
, size := 48 )
gap> P14 := Group(R.generators);
<matrix group with 4 generators>
gap> Append(names,["ordnung.48/(2)^4(6)^2/words.group.1654"]);
gap> Append(GROUPS,[P14]);
gap> R := CaratReadBravaisFile("ordnung.6/(6)^6/min.302");
rec(
generators := [ [ [ 0, 0, 1, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0,
0, 0 ], [ 0, 1, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, -1 ] ],
[ [ 0, 0, -1, 0, 0, 0 ], [ 0, -1, 0, 1, 0, 0 ], [ 1, 0, -1, 0, 0, 0 ],
[ 0, -1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ]
], size := 6 )
gap> P15 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.6/(6)^6/words.min.302"]);
gap> Append(GROUPS,[P15]);
gap> Print(GROUPS,"\n");
[ Group(
[ [ [ 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, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ],
[ [ 0, -1, 0, 0, 0, 0 ], [ 1, -1, 0, 0, 0, 0 ], [ -1, 0, 0, -1, 0, 0 ],
[ -1, 1, 1, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ]
] ]),
Group([ [ [ -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, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ],
[ [ -1, 1, 0, 0, 0, 0 ], [ -1, 0, 0, 0, 0, 0 ], [ 1, 0, -1, 1, 0, 0 ],
[ 1, -1, -1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ]
] ]),
Group([ [ [ -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, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, -1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ -1, 0, 1, -1, 0, 0 ],
[ -1, 1, 1, 0, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ]
] ]),
Group([ [ [ -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, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ]
,
[ [ 1, -1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ -1, 0, 1, -1, 0, 0 ],
[ -1, 1, 1, 0, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ]
] ]),
Group([ [ [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, -1, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ],
[ 1, -1, 0, 0, 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, -1, 1, 0, 0 ],
[ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ]
] ]),
Group([ [ [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 1, -1, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ],
[ 1, -1, 0, 0, 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, 1, -1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ]
]),
Group([ [ [ -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, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, -1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ -1, 0, 1, -1, 0, 0 ],
[ -1, 1, 1, 0, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ]
] ]),
Group([ [ [ 1, 1, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 0, -1, 1, 0, 0 ]
, [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1 ] ],
[ [ -1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 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, -1, 1, 0, 0 ],
[ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ]
] ]),
Group([ [ [ 0, 0, -1, 1, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0
], [ 1, -1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, -1 ] ],
[ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ]
,
[ [ 0, -1, 0, 0, 0, 0 ], [ 1, -1, 0, 0, 0, 0 ], [ 0, 0, -1, 1, 0, 0 ],
[ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ]
] ]),
Group([ [ [ 0, 0, -1, 1, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0
], [ 1, -1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, -1 ] ],
[ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ]
,
[ [ 0, 1, 0, 0, 0, 0 ], [ -1, 1, 0, 0, 0, 0 ], [ 0, 0, 1, -1, 0, 0 ],
[ 0, 0, 1, 0, 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, -1, 0, 0 ],
[ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ]
,
[ [ -1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], [ 0, 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, -1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ]
] ]),
Group([ [ [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, -1, 1, 0, 0 ], [ -1, 0, 0, 0, 0, 0
], [ -1, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, -1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ]
]),
Group([ [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ],
[ [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, -1, 1, 0, 0 ], [ -1, 0, 0, 0, 0, 0 ],
[ -1, 1, 0, 0, 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, 1, -1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ]
]),
Group([ [ [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, -1, 1, 0, 0 ], [ -1, 0, 0, 0, 0, 0
], [ -1, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ],
[ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ]
,
[ [ 1, -1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ]
]),
Group([ [ [ 0, 0, 1, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ]
,
[ [ 0, 0, -1, 0, 0, 0 ], [ 0, -1, 0, 1, 0, 0 ], [ 1, 0, -1, 0, 0, 0 ],
[ 0, -1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ]
]) ]
gap> Print(names,"\n");
[ "ordnung.12/(2)^2(6)^4/words.group.1641",
"ordnung.12/(2)^2(6)^4/words.group.1642",
"ordnung.12/(2)^2(6)^4/words.group.1643",
"ordnung.12/(2)^2(6)^4/words.group.1644",
"ordnung.12/(2)^4(6)^2/words.group.1645",
"ordnung.12/(2)^4(6)^2/words.group.1646",
"ordnung.12/(6)^6/words.group.1647",
"ordnung.24/(2)^2(6)^4/words.group.1648",
"ordnung.24/(2)^4(6)^2/words.group.1649",
"ordnung.24/(2)^4(6)^2/words.group.1650",
"ordnung.24/(2)^4(6)^2/words.group.1651",
"ordnung.24/(2)^4(6)^2/words.group.1652",
"ordnung.24/(2)^4(6)^2/words.group.1653",
"ordnung.48/(2)^4(6)^2/words.group.1654", "ordnung.6/(6)^6/words.min.302" ]
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;
[ x2^3, x2^2 ]
[ x1, x2^2 ]
[ x1*x2^3, x2^2 ]
[ x2^3, x1 ]
[ x2^3, x2^2 ]
[ x2^2*x1, x2^2 ]
[ x1*x2, x2^2 ]
[ x2^3, x2^2*x1 ]
[ x2^3, x2^2 ]
[ x1*x2^2, x2^2 ]
[ x2*x1, x2^2 ]
[ x2^3, x1*x2^2 ]
[ x2^3, x2^2 ]
[ x1*x2^2, x2^2 ]
[ x2*x1, x2^2 ]
[ x2^3, x1*x2^2 ]
[ x2^3, x2^2 ]
[ x1, x2^2 ]
[ x1*x2^3, x2^2 ]
[ x2^3, x1 ]
[ x2^3, x2^2 ]
[ x1, x2^2 ]
[ x1*x2^3, x2^2 ]
[ x2^3, x1 ]
[ x2^3, x2^2 ]
[ x1*x2^2, x2^2 ]
[ x2*x1, x2^2 ]
[ x2^3, x1*x2^2 ]
[ x3^3, x1*x2, x3^2 ]
[ x3^3, x1, x3^2 ]
[ x3^3, x2, x3^2 ]
[ x1*x2, x1, x3^2 ]
[ x1*x3^3, x1*x2, x3^2 ]
[ x1*x2*x3^3, x1, x3^2 ]
[ x1*x3^3, x2, x3^2 ]
[ x3^3, x1*x2, x1 ]
[ x3^3, x2, x3^2 ]
[ x3^3, x1, x3^2 ]
[ x3^3, x1*x2, x3^2 ]
[ x2, x1, x3^2 ]
[ x1*x3^3, x2, x3^2 ]
[ x2*x3^3, x1, x3^2 ]
[ x1*x3^3, x1*x2, x3^2 ]
[ x3^3, x2, x1 ]
[ x3^3, x2, x3^2 ]
[ x3^3, x1, x3^2 ]
[ x3^3, x1*x2, x3^2 ]
[ x2, x1, x3^2 ]
[ x1*x3^3, x2, x3^2 ]
[ x2*x3^3, x1, x3^2 ]
[ x1*x3^3, x1*x2, x3^2 ]
[ x3^3, x2, x1 ]
[ x3^3, x1*x2, x3^2 ]
[ x3^3, x1, x3^2 ]
[ x3^3, x2, x3^2 ]
[ x1*x2, x1, x3^2 ]
[ x1*x3^3, x1*x2, x3^2 ]
[ x1*x2*x3^3, x1, x3^2 ]
[ x1*x3^3, x2, x3^2 ]
[ x3^3, x1*x2, x1 ]
[ x3^3, x2, x3^2 ]
[ x3^3, x1, x3^2 ]
[ x3^3, x1*x2, x3^2 ]
[ x2, x1, x3^2 ]
[ x1*x3^3, x2, x3^2 ]
[ x2*x3^3, x1, x3^2 ]
[ x1*x3^3, x1*x2, x3^2 ]
[ x3^3, x2, x1 ]
[ x3^3, x1*x2, x3^2 ]
[ x3^3, x1, x3^2 ]
[ x3^3, x2, x3^2 ]
[ x1*x2, x1, x3^2 ]
[ x1*x3^3, x1*x2, x3^2 ]
[ x1*x2*x3^3, x1, x3^2 ]
[ x1*x3^3, x2, x3^2 ]
[ x3^3, x1*x2, x1 ]
[ x4^3, x2*x3, x2, x4^2 ]
[ x4^3, x2*x3, x1, x4^2 ]
[ x4^3, x2*x3, x1*x2, x4^2 ]
[ x4^3, x2, x1, x4^2 ]
[ x4^3, x1*x2*x3, x2, x4^2 ]
[ x4^3, x3, x1, x4^2 ]
[ x4^3, x1*x2*x3, x1*x2, x4^2 ]
[ x2*x3, x2, x1, x4^2 ]
[ x1*x4^3, x2*x3, x2, x4^2 ]
[ x2*x4^3, x2*x3, x1, x4^2 ]
[ x1*x4^3, x2*x3, x1*x2, x4^2 ]
[ x2*x3*x4^3, x2, x1, x4^2 ]
[ x1*x4^3, x1*x2*x3, x2, x4^2 ]
[ x2*x4^3, x3, x1, x4^2 ]
[ x1*x4^3, x1*x2*x3, x1*x2, x4^2 ]
[ x4^3, x2*x3, x2, x1 ]
[ x1*x2*x1 ]
[ x2*x1 ]
gap> LogTo();