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/(1)^2(24)^2/group.1623");
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, 1, -1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -1 ], [ 0, 0, 0, 0, 1, -1 ]
] ], size := 12 )
gap> P1 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.12/(1)^2(24)^2/words.group.1623"]);
gap> Append(GROUPS,[P1]);
gap> R := CaratReadBravaisFile("ordnung.18/(1)^2(3)^2(6)^1(18)^1/group.1624");
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, 1 ],
[ 0, 0, 0, 0, -1, 0 ] ],
[ [ 0, 1, 0, 0, 0, 0 ], [ -1, 1, 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 := 18 )
gap> P2 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.18/(1)^2(3)^2(6)^1(18)^1/words.group.1624"]);
gap> Append(GROUPS,[P2]);
gap> R := CaratReadBravaisFile("ordnung.18/(1)^2(3)^2(6)^1(18)^1/group.1625");
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, 1 ],
[ 0, 0, 0, 0, -1, 0 ] ],
[ [ 0, -1, 0, 0, 0, 0 ], [ 1, -1, 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 := 18 )
gap> P3 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.18/(1)^2(3)^2(6)^1(18)^1/words.group.1625"]);
gap> Append(GROUPS,[P3]);
gap> R := CaratReadBravaisFile("ordnung.18/(1)^2(6)^2/group.1626");
rec(
generators := [ [ [ -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 ] ],
[ [ -1, 0, 0, 0, 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, -1 ]
] ], size := 18 )
gap> P4 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.18/(1)^2(6)^2/words.group.1626"]);
gap> Append(GROUPS,[P4]);
gap> R := CaratReadBravaisFile("ordnung.18/(1)^2(6)^2/group.1627");
rec(
generators := [ [ [ 0, -1, 0, 0, 0, 0 ], [ 1, -1, 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 ] ],
[ [ 1, 0, 0, 0, 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, 1 ] ]
], size := 18 )
gap> P5 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.18/(1)^2(6)^2/words.group.1627"]);
gap> Append(GROUPS,[P5]);
gap> R := CaratReadBravaisFile("ordnung.18/(3)^2(6)^2/group.1628");
rec(
generators := [ [ [ 0, -1, 0, 0, 0, 0 ], [ 1, -1, 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 ] ],
[ [ -1, 0, 0, 0, 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, 1 ]
] ], size := 18 )
gap> P6 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.18/(3)^2(6)^2/words.group.1628"]);
gap> Append(GROUPS,[P6]);
gap> R := CaratReadBravaisFile("ordnung.36/(1)^2(3)^2(6)^1(18)^1/group.1629");
rec(
generators := [ [ [ 0, -1, 0, 0, 0, 0 ], [ 1, -1, 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 ] ],
[ [ -1, 0, 0, 0, 0, 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, 1, 0 ]
] ], size := 36 )
gap> P7 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.36/(1)^2(3)^2(6)^1(18)^1/words.group.1629"]);
gap> Append(GROUPS,[P7]);
gap> R := CaratReadBravaisFile("ordnung.36/(1)^2(6)^2/group.1630");
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, -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 := 36 )
gap> P8 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.36/(1)^2(6)^2/words.group.1630"]);
gap> Append(GROUPS,[P8]);
gap> R := CaratReadBravaisFile("ordnung.36/(1)^3(3)^1(6)^2/group.1631");
rec(
generators := [ [ [ 0, -1, 0, 0, 0, 0 ], [ 1, -1, 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 ] ],
[ [ -1, 0, 0, 0, 0, 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, -1, 0 ]
] ], size := 36 )
gap> P9 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.36/(1)^3(3)^1(6)^2/words.group.1631"]);
gap> Append(GROUPS,[P9]);
gap> R := CaratReadBravaisFile("ordnung.36/(1)^3(3)^1(6)^2/group.1632");
rec(
generators := [ [ [ 0, -1, 0, 0, 0, 0 ], [ 1, -1, 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 ] ],
[ [ 1, 0, 0, 0, 0, 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, 1, 0 ] ]
], size := 36 )
gap> P10 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.36/(1)^3(3)^1(6)^2/words.group.1632"]);
gap> Append(GROUPS,[P10]);
gap> R := CaratReadBravaisFile("ordnung.36/(1)^3(3)^1(6)^2/group.1633");
rec(
generators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ -1, 1, 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 ] ],
[ [ 1, 0, 0, 0, 0, 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, 1, 0 ] ]
], size := 36 )
gap> P11 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.36/(1)^3(3)^1(6)^2/words.group.1633"]);
gap> Append(GROUPS,[P11]);
gap> R := CaratReadBravaisFile("ordnung.6/(1)^2(24)^2/min.296");
rec(
generators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ -1, 1, 0, 0, 0, 0 ], [ 0, 0, 0,
-1, 0, 0 ], [ 0, 0, 1, 1, 0, 0 ], [ 0, 0, 0, 0, -1, -1 ],
[ 0, 0, 0, 0, 1, 0 ] ] ], size := 6 )
gap> P12 := Group(R.generators);
<matrix group with 1 generators>
gap> Append(names,["ordnung.6/(1)^2(24)^2/words.min.296"]);
gap> Append(GROUPS,[P12]);
gap> R := CaratReadBravaisFile("ordnung.6/(1)^2(24)^2/min.297");
rec(
generators := [ [ [ 0, -1, 0, 0, 0, 0 ], [ 1, -1, 0, 0, 0, 0 ], [ 0, 0, 0,
1, 0, 0 ], [ 0, 0, -1, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 1 ],
[ 0, 0, 0, 0, -1, 0 ] ] ], size := 6 )
gap> P13 := Group(R.generators);
<matrix group with 1 generators>
gap> Append(names,["ordnung.6/(1)^2(24)^2/words.min.297"]);
gap> Append(GROUPS,[P13]);
gap> R := CaratReadBravaisFile("ordnung.72/(1)^3(3)^1(6)^2/group.1634");
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, 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 ] ],
[ [ -1, 0, 0, 0, 0, 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, -1, 0 ]
] ], size := 72 )
gap> P14 := Group(R.generators);
<matrix group with 3 generators>
gap> Append(names,["ordnung.72/(1)^3(3)^1(6)^2/words.group.1634"]);
gap> Append(GROUPS,[P14]);
gap> R := CaratReadBravaisFile("ordnung.9/(3)^2(6)^2/min.298");
rec(
generators := [ [ [ 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 ] ],
[ [ 1, 0, 0, 0, 0, 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, -1, 0 ]
] ], size := 9 )
gap> P15 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.9/(3)^2(6)^2/words.min.298"]);
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, 1, 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, -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, 1 ], [ 0, 0, 0, 0, -1, 0 ] ]
,
[ [ 0, 1, 0, 0, 0, 0 ], [ -1, 1, 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, 0, 0, 0, 0, 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, -1, 0 ] ]
,
[ [ 0, -1, 0, 0, 0, 0 ], [ 1, -1, 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 ], [ -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 ] ],
[ [ -1, 0, 0, 0, 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, -1 ]
] ]),
Group([ [ [ 0, -1, 0, 0, 0, 0 ], [ 1, -1, 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 ] ],
[ [ 1, 0, 0, 0, 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, 1 ] ]
]),
Group([ [ [ 0, -1, 0, 0, 0, 0 ], [ 1, -1, 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 ] ],
[ [ -1, 0, 0, 0, 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, 1 ]
] ]),
Group([ [ [ 0, -1, 0, 0, 0, 0 ], [ 1, -1, 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 ] ],
[ [ -1, 0, 0, 0, 0, 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, 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, 0, -1 ],
[ 0, 0, 0, 0, 1, -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, -1, 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 ] ],
[ [ -1, 0, 0, 0, 0, 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, -1, 0 ]
] ]),
Group([ [ [ 0, -1, 0, 0, 0, 0 ], [ 1, -1, 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 ] ],
[ [ 1, 0, 0, 0, 0, 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, 1, 0 ] ]
]),
Group([ [ [ 0, 1, 0, 0, 0, 0 ], [ -1, 1, 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 ] ],
[ [ 1, 0, 0, 0, 0, 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, 1, 0 ] ]
]),
Group([ [ [ 0, 1, 0, 0, 0, 0 ], [ -1, 1, 0, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ]
, [ 0, 0, 1, 1, 0, 0 ], [ 0, 0, 0, 0, -1, -1 ],
[ 0, 0, 0, 0, 1, 0 ] ] ]),
Group([ [ [ 0, -1, 0, 0, 0, 0 ], [ 1, -1, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0 ], [ 0, 0, -1, -1, 0, 0 ], [ 0, 0, 0, 0, 1, 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 ] ]
,
[ [ -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 ] ],
[ [ -1, 0, 0, 0, 0, 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, -1, 0 ]
] ]),
Group([ [ [ 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 ] ],
[ [ 1, 0, 0, 0, 0, 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, -1, 0 ]
] ]) ]
gap> Print(names,"\n");
[ "ordnung.12/(1)^2(24)^2/words.group.1623",
"ordnung.18/(1)^2(3)^2(6)^1(18)^1/words.group.1624",
"ordnung.18/(1)^2(3)^2(6)^1(18)^1/words.group.1625",
"ordnung.18/(1)^2(6)^2/words.group.1626",
"ordnung.18/(1)^2(6)^2/words.group.1627",
"ordnung.18/(3)^2(6)^2/words.group.1628",
"ordnung.36/(1)^2(3)^2(6)^1(18)^1/words.group.1629",
"ordnung.36/(1)^2(6)^2/words.group.1630",
"ordnung.36/(1)^3(3)^1(6)^2/words.group.1631",
"ordnung.36/(1)^3(3)^1(6)^2/words.group.1632",
"ordnung.36/(1)^3(3)^1(6)^2/words.group.1633",
"ordnung.6/(1)^2(24)^2/words.min.296", "ordnung.6/(1)^2(24)^2/words.min.297"
, "ordnung.72/(1)^3(3)^1(6)^2/words.group.1634",
"ordnung.9/(3)^2(6)^2/words.min.298" ]
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, x2^4 ]
[ x1, x2^4 ]
[ x1*x2^3, x2^4 ]
[ x2^3, x1 ]
[ x2^2, x1^2 ]
[ x2^3, x1^2 ]
[ x2^3, x2^2 ]
[ x2^4, x1^2 ]
[ x2^3, x1^2 ]
[ x2^3, x2^4 ]
[ x2^2, x1 ]
[ x2^3, x2^2 ]
[ x2^3, x1 ]
[ x2^3, x1^2*x2^2 ]
[ x2^3, x1*x2^2 ]
[ x2^2, x1 ]
[ x2^3, x2^2 ]
[ x2^3, x1 ]
[ x2^3, x1^2*x2^2 ]
[ x2^3, x1*x2^2 ]
[ x2^2, x1 ]
[ x2^3, x2^2 ]
[ x2^3, x1 ]
[ x2^3, x1^2*x2^2 ]
[ x2^3, x1*x2^2 ]
[ x1^3*x2^3, x1^2, x2^2 ]
[ x1^3, x1^2, x2^2 ]
[ x2^3, x1^2, x2^2 ]
[ x1^3*x2^3, x1^3, x2^2 ]
[ x1^3*x2^3, x1^3, x1^2 ]
[ x2^3, x2^4, x1^2 ]
[ x1^3, x2^4, x1^2 ]
[ x1^3*x2^3, x2^4, x1^2 ]
[ x2^3, x1^3, x2^4 ]
[ x2^3, x1^3, x1^2 ]
[ x2^3, x1^3, x1^4*x2^4 ]
[ x2^3, x1^3, x1^2*x2^4 ]
[ x2^3, x1^4, x2^2 ]
[ x1^3, x1^4, x2^2 ]
[ x1^3*x2^3, x1^4, x2^2 ]
[ x2^3, x1^3, x2^2 ]
[ x2^3, x1^3, x1^4 ]
[ x1^3*x2^3, x1^2, x2^2 ]
[ x1^3, x1^2, x2^2 ]
[ x2^3, x1^2, x2^2 ]
[ x1^3*x2^3, x1^3, x2^2 ]
[ x1^3*x2^3, x1^3, x1^2 ]
[ x1^3*x2^3, x1^2, x2^2 ]
[ x1^3, x1^2, x2^2 ]
[ x2^3, x1^2, x2^2 ]
[ x1^3*x2^3, x1^3, x2^2 ]
[ x1^3*x2^3, x1^3, x1^2 ]
[ x1^3 ]
[ x1^2 ]
[ x1^3 ]
[ x1^2 ]
[ x3^3, x1*x2^2*x3^2*x2, x2^4, x3^2 ]
[ x3^3, x1, x2^4, x3^2 ]
[ x3^3, x2^2*x3^2*x2, x2^4, x3^2 ]
[ x1*x2^2*x3^2*x2, x1, x2^4, x3^2 ]
[ x1*x3^3, x1*x2^2*x3^2*x2, x2^4, x3^2 ]
[ x1*x2^3*x3, x1, x2^4, x3^2 ]
[ x1*x3^3, x2^2*x3^2*x2, x2^4, x3^2 ]
[ x3^3, x1*x2^2*x3^2*x2, x1, x3^2 ]
[ x3^3, x1*x2^2*x3^2*x2, x1, x2^4 ]
[ x2 ]
[ x1 ]
[ x1^2*x2 ]
[ x1*x2 ]
gap> LogTo();