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)^4(6)^2/min.303");
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, 0, -1 ],
[ 0, 0, 0, 0, 1, 0 ] ],
[ [ -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 := 12 )
gap> P1 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.12/(2)^4(6)^2/words.min.303"]);
gap> Append(GROUPS,[P1]);
gap> R := CaratReadBravaisFile("ordnung.24/(2)^4(6)^2/group.1655");
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, 0, -1 ],
[ 0, 0, 0, 0, 1, 0 ] ],
[ [ 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> P2 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.24/(2)^4(6)^2/words.group.1655"]);
gap> Append(GROUPS,[P2]);
gap> R := CaratReadBravaisFile("ordnung.24/(2)^4(6)^2/group.1656");
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, 0, -1 ], [ 0, 0, 0, 0, 1, 0 ]
] ], size := 24 )
gap> P3 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.24/(2)^4(6)^2/words.group.1656"]);
gap> Append(GROUPS,[P3]);
gap> R := CaratReadBravaisFile("ordnung.24/(2)^4(6)^2/group.1657");
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, 0, -1 ], [ 0, 0, 0, 0, 1, 0 ] ]
], size := 24 )
gap> P4 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.24/(2)^4(6)^2/words.group.1657"]);
gap> Append(GROUPS,[P4]);
gap> R := CaratReadBravaisFile("ordnung.24/(2)^6(6)^2/group.1658");
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, 0, 1 ],
[ 0, 0, 0, 0, 1, 0 ] ],
[ [ -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> P5 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.24/(2)^6(6)^2/words.group.1658"]);
gap> Append(GROUPS,[P5]);
gap> R := CaratReadBravaisFile("ordnung.24/(2)^6(6)^2/group.1659");
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, 0, 1 ],
[ 0, 0, 0, 0, 1, 0 ] ],
[ [ 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> P6 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.24/(2)^6(6)^2/words.group.1659"]);
gap> Append(GROUPS,[P6]);
gap> R := CaratReadBravaisFile("ordnung.24/(2)^6(6)^2/min.304");
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 ], [ 0, 0, 0, 1, 0, 0 ],
[ 0, 0, -1, -1, 0, 0 ], [ 0, 0, 0, 0, 0, -1 ], [ 0, 0, 0, 0, 1, 0 ]
] ], size := 24 )
gap> P7 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.24/(2)^6(6)^2/words.min.304"]);
gap> Append(GROUPS,[P7]);
gap> R := CaratReadBravaisFile("ordnung.24/(2)^6(6)^2/min.305");
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, 0, 1 ],
[ 0, 0, 0, 0, 1, 0 ] ],
[ [ 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 ]
] ], size := 24 )
gap> P8 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.24/(2)^6(6)^2/words.min.305"]);
gap> Append(GROUPS,[P8]);
gap> R := CaratReadBravaisFile("ordnung.48/(2)^4(6)^2/group.1660");
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, 0, -1 ], [ 0, 0, 0, 0, 1, 0 ]
] ], size := 48 )
gap> P9 := Group(R.generators);
<matrix group with 3 generators>
gap> Append(names,["ordnung.48/(2)^4(6)^2/words.group.1660"]);
gap> Append(GROUPS,[P9]);
gap> R := CaratReadBravaisFile("ordnung.48/(2)^6(6)^2/group.1661");
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, 0, 1 ], [ 0, 0, 0, 0, 1, 0 ] ],
[ [ 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> P10 := Group(R.generators);
<matrix group with 3 generators>
gap> Append(names,["ordnung.48/(2)^6(6)^2/words.group.1661"]);
gap> Append(GROUPS,[P10]);
gap> R := CaratReadBravaisFile("ordnung.48/(2)^6(6)^2/group.1662");
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, 0, -1 ], [ 0, 0, 0, 0, 1, 0 ]
] ], size := 48 )
gap> P11 := Group(R.generators);
<matrix group with 3 generators>
gap> Append(names,["ordnung.48/(2)^6(6)^2/words.group.1662"]);
gap> Append(GROUPS,[P11]);
gap> R := CaratReadBravaisFile("ordnung.48/(2)^6(6)^2/group.1663");
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, 0, 1 ], [ 0, 0, 0, 0, 1, 0 ] ]
], size := 48 )
gap> P12 := Group(R.generators);
<matrix group with 3 generators>
gap> Append(names,["ordnung.48/(2)^6(6)^2/words.group.1663"]);
gap> Append(GROUPS,[P12]);
gap> R := CaratReadBravaisFile("ordnung.48/(2)^6(6)^2/group.1664");
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 ] ],
[ [ 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, 0, 1 ], [ 0, 0, 0, 0, 1, 0 ] ],
[ [ -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> P13 := Group(R.generators);
<matrix group with 3 generators>
gap> Append(names,["ordnung.48/(2)^6(6)^2/words.group.1664"]);
gap> Append(GROUPS,[P13]);
gap> R := CaratReadBravaisFile("ordnung.48/(2)^6(6)^2/group.1665");
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, 0, 1 ],
[ 0, 0, 0, 0, 1, 0 ] ],
[ [ 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 := 48 )
gap> P14 := Group(R.generators);
<matrix group with 3 generators>
gap> Append(names,["ordnung.48/(2)^6(6)^2/words.group.1665"]);
gap> Append(GROUPS,[P14]);
gap> R := CaratReadBravaisFile("ordnung.96/(2)^6(6)^2/group.1666");
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, 0, 1 ], [ 0, 0, 0, 0, 1, 0 ] ]
], size := 96 )
gap> P15 := Group(R.generators);
<matrix group with 4 generators>
gap> Append(names,["ordnung.96/(2)^6(6)^2/words.group.1666"]);
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, 0, -1 ], [ 0, 0, 0, 0, 1, 0 ] ]
,
[ [ -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, 0, -1 ], [ 0, 0, 0, 0, 1, 0 ] ]
,
[ [ 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, 0, -1 ], [ 0, 0, 0, 0, 1, 0 ]
] ]),
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, 0, -1 ], [ 0, 0, 0, 0, 1, 0 ] ]
]),
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, 0, 1 ], [ 0, 0, 0, 0, 1, 0 ] ],
[ [ -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, 0, 1 ], [ 0, 0, 0, 0, 1, 0 ] ],
[ [ 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 ], [ 0, 0, 0, 1, 0, 0 ],
[ 0, 0, -1, -1, 0, 0 ], [ 0, 0, 0, 0, 0, -1 ], [ 0, 0, 0, 0, 1, 0 ]
] ]),
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, 0, 1 ],
[ 0, 0, 0, 0, 1, 0 ] ],
[ [ 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 ]
] ]),
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, 0, -1 ], [ 0, 0, 0, 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, 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, 0, 1 ], [ 0, 0, 0, 0, 1, 0 ] ],
[ [ 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, 0, -1 ], [ 0, 0, 0, 0, 1, 0 ]
] ]),
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, 0, 1 ], [ 0, 0, 0, 0, 1, 0 ] ]
]),
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 ] ],
[ [ 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, 0, 1 ], [ 0, 0, 0, 0, 1, 0 ] ],
[ [ -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, 0, 1 ],
[ 0, 0, 0, 0, 1, 0 ] ],
[ [ 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, 0, 1 ], [ 0, 0, 0, 0, 1, 0 ] ]
]) ]
gap> Print(names,"\n");
[ "ordnung.12/(2)^4(6)^2/words.min.303",
"ordnung.24/(2)^4(6)^2/words.group.1655",
"ordnung.24/(2)^4(6)^2/words.group.1656",
"ordnung.24/(2)^4(6)^2/words.group.1657",
"ordnung.24/(2)^6(6)^2/words.group.1658",
"ordnung.24/(2)^6(6)^2/words.group.1659",
"ordnung.24/(2)^6(6)^2/words.min.304", "ordnung.24/(2)^6(6)^2/words.min.305"
, "ordnung.48/(2)^4(6)^2/words.group.1660",
"ordnung.48/(2)^6(6)^2/words.group.1661",
"ordnung.48/(2)^6(6)^2/words.group.1662",
"ordnung.48/(2)^6(6)^2/words.group.1663",
"ordnung.48/(2)^6(6)^2/words.group.1664",
"ordnung.48/(2)^6(6)^2/words.group.1665",
"ordnung.96/(2)^6(6)^2/words.group.1666" ]
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;
[ x1^2, x1^3*x2*x1 ]
[ x1*x2, x1^2 ]
[ x2^3, x1^2, x2^2 ]
[ x1, x1^2, x2^2 ]
[ x1*x2^3, x1^2, x2^2 ]
[ x2^3, x1, x1^2 ]
[ x1*x2*x1*x2^4, x1*x2*x1*x2, x1*x2*x1*x2^3 ]
[ x1, x1*x2*x1*x2, x1*x2*x1*x2^3 ]
[ x2*x1*x2^4, x1*x2*x1*x2, x1*x2*x1*x2^3 ]
[ x1*x2*x1*x2^4, x1, x1*x2*x1*x2 ]
[ x1*x2*x1*x2^4, x1*x2*x1*x2, x1*x2*x1*x2^3 ]
[ x1, x1*x2*x1*x2, x1*x2*x1*x2^3 ]
[ x2*x1*x2^4, x1*x2*x1*x2, x1*x2*x1*x2^3 ]
[ x1*x2*x1*x2^4, 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 ]
[ 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*x2^3*x1, x2^6, x1*x2^4*x1 ]
[ x1*x2^4, x2^6, x1*x2^4*x1 ]
[ x2^5*x1, x2^6, x1*x2^4*x1 ]
[ x1*x2^3*x1, x1*x2^4, x2^6 ]
[ 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, 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,
x2*x1*x2*x1*x2*x1*x2*x1 ]
[ x1*x2*x1*x2*x1*x2*x1, x1, x1*x2*x1*x2*x1*x2*x1*x2*x1*x2*x1*x2 ]
[ x1*x3*x1*x3^4, x2, x1*x3*x1*x3, x1*x3*x1*x3^3 ]
[ x1*x3*x1*x3^4, x1, x1*x3*x1*x3, x1*x3*x1*x3^3 ]
[ x1*x3*x1*x3^4, x1*x2, x1*x3*x1*x3, x1*x3*x1*x3^3 ]
[ x2, x1, x1*x3*x1*x3, x1*x3*x1*x3^3 ]
[ x3*x1*x3^4, x2, x1*x3*x1*x3, x1*x3*x1*x3^3 ]
[ x1*x2*x3*x1*x3^4, x1, x1*x3*x1*x3, x1*x3*x1*x3^3 ]
[ x3*x1*x3^4, x1*x2, x1*x3*x1*x3, x1*x3*x1*x3^3 ]
[ x1*x3*x1*x3^4, x2, x1, x1*x3*x1*x3 ]
[ x3^3, x2, x1*x2*x1*x2, x3^2 ]
[ x3^3, x1, x1*x2*x1*x2, x3^2 ]
[ x3^3, x2*x1, x1*x2*x1*x2, x3^2 ]
[ x2, x1, x1*x2*x1*x2, x3^2 ]
[ x1*x3^3, x2, x1*x2*x1*x2, x3^2 ]
[ x2*x3^3, x1, x1*x2*x1*x2, x3^2 ]
[ x1*x3^3, x2*x1, x1*x2*x1*x2, x3^2 ]
[ x3^3, x2, x1, x1*x2*x1*x2 ]
[ x2*x3^3*x2, x1, x3^6, x2*x3^4*x2 ]
[ x2*x3^3*x2, x2, x3^6, x2*x3^4*x2 ]
[ x2*x3^3*x2, x1*x2, x3^6, x2*x3^4*x2 ]
[ x1, x2, x3^6, x2*x3^4*x2 ]
[ x2*x3^3, x1, x3^6, x2*x3^4*x2 ]
[ x1*x2*x3^3*x2, x2, x3^6, x2*x3^4*x2 ]
[ x2*x3^3, x1*x2, x3^6, x2*x3^4*x2 ]
[ x2*x3^3*x2, x1, x2, x3^6 ]
[ x3^3, x1, x1*x2*x3*x1*x2*x3, x3^2 ]
[ x3^3, x2, x1*x2*x3*x1*x2*x3, x3^2 ]
[ x3^3, x1*x2, x1*x2*x3*x1*x2*x3, x3^2 ]
[ x1, x2, x1*x2*x3*x1*x2*x3, x3^2 ]
[ x3*x2*x3^2, x1, x1*x2*x3*x1*x2*x3, x3^2 ]
[ x1*x3^3, x2, x1*x2*x3*x1*x2*x3, x3^2 ]
[ x3*x2*x3^2, x1*x2, x1*x2*x3*x1*x2*x3, x3^2 ]
[ x3^3, x1, x2, x1*x2*x3*x1*x2*x3 ]
[ x3^3, x1, x2*x3*x2*x3, x3^2 ]
[ x3^3, x2, x2*x3*x2*x3, x3^2 ]
[ x3^3, x1*x2, x2*x3*x2*x3, x3^2 ]
[ x1, x2, x2*x3*x2*x3, x3^2 ]
[ x3^3*x2, x1, x2*x3*x2*x3, x3^2 ]
[ x1*x3^3, x2, x2*x3*x2*x3, x3^2 ]
[ x3^3*x2, x1*x2, x2*x3*x2*x3, x3^2 ]
[ x3^3, x1, x2, x2*x3*x2*x3 ]
[ x3^3, x2, x1*x2*x1*x2, x3^2 ]
[ x3^3, x1, x1*x2*x1*x2, x3^2 ]
[ x3^3, x2*x1, x1*x2*x1*x2, x3^2 ]
[ x2, x1, x1*x2*x1*x2, x3^2 ]
[ x2*x1*x2*x3^3, x2, x1*x2*x1*x2, x3^2 ]
[ x2*x3^3, x1, x1*x2*x1*x2, x3^2 ]
[ x2*x1*x2*x3^3, x2*x1, x1*x2*x1*x2, x3^2 ]
[ x3^3, x2, x1, x1*x2*x1*x2 ]
[ x4^3, x1, x2, x1*x3*x4*x1*x3*x4, x4^2 ]
[ x4^3, x1, x3, x1*x3*x4*x1*x3*x4, x4^2 ]
[ x4^3, x1, x2*x3, x1*x3*x4*x1*x3*x4, x4^2 ]
[ x4^3, x2, x3, x1*x3*x4*x1*x3*x4, x4^2 ]
[ x4^3, x1*x3, x2, x1*x3*x4*x1*x3*x4, x4^2 ]
[ x4^3, x1*x2, x3, x1*x3*x4*x1*x3*x4, x4^2 ]
[ x4^3, x1*x3, x2*x3, x1*x3*x4*x1*x3*x4, x4^2 ]
[ x1, x2, x3, x1*x3*x4*x1*x3*x4, x4^2 ]
[ x4*x3*x4^2, x1, x2, x1*x3*x4*x1*x3*x4, x4^2 ]
[ x2*x4^3, x1, x3, x1*x3*x4*x1*x3*x4, x4^2 ]
[ x4*x3*x4^2, x1, x2*x3, x1*x3*x4*x1*x3*x4, x4^2 ]
[ x1*x4^3, x2, x3, x1*x3*x4*x1*x3*x4, x4^2 ]
[ x4*x3*x4^2, x1*x3, x2, x1*x3*x4*x1*x3*x4, x4^2 ]
[ x2*x4^3, x1*x2, x3, x1*x3*x4*x1*x3*x4, x4^2 ]
[ x4*x3*x4^2, x1*x3, x2*x3, x1*x3*x4*x1*x3*x4, x4^2 ]
[ x4^3, x1, x2, x3, x1*x3*x4*x1*x3*x4 ]
gap> LogTo();