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(3)^2(18)^1(54)^1/group.1698");
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, -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 := 12 )
gap> P1 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.12/(1)^2(3)^2(18)^1(54)^1/words.group.1698"]);
gap> Append(GROUPS,[P1]);
gap> R := CaratReadBravaisFile("ordnung.12/(1)^2(3)^2(6)^1(18)^1/group.1699");
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 ] ],
[ [ 0, -1, 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 := 12 )
gap> P2 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.12/(1)^2(3)^2(6)^1(18)^1/words.group.1699"]);
gap> Append(GROUPS,[P2]);
gap> R := CaratReadBravaisFile("ordnung.12/(1)^2(3)^2(6)^1(18)^1/group.1700");
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, 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 := 12 )
gap> P3 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.12/(1)^2(3)^2(6)^1(18)^1/words.group.1700"]);
gap> Append(GROUPS,[P3]);
gap> R := CaratReadBravaisFile("ordnung.12/(1)^2(3)^2(6)^1(18)^1/group.1701");
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 ] ],
[ [ 0, 1, 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 := 12 )
gap> P4 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.12/(1)^2(3)^2(6)^1(18)^1/words.group.1701"]);
gap> Append(GROUPS,[P4]);
gap> R := CaratReadBravaisFile("ordnung.12/(1)^2(3)^2(6)^1(18)^1/group.1702");
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, -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 := 12 )
gap> P5 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.12/(1)^2(3)^2(6)^1(18)^1/words.group.1702"]);
gap> Append(GROUPS,[P5]);
gap> R := CaratReadBravaisFile("ordnung.12/(1)^2(6)^1(54)^1/group.1703");
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, 0, 0, 0 ],
[ 0, 0, 0, -1, 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/(1)^2(6)^1(54)^1/words.group.1703"]);
gap> Append(GROUPS,[P6]);
gap> R := CaratReadBravaisFile("ordnung.12/(1)^2(6)^2/group.1704");
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, 0, 0, 0 ],
[ 0, 0, 0, 1, 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/(1)^2(6)^2/words.group.1704"]);
gap> Append(GROUPS,[P7]);
gap> R := CaratReadBravaisFile("ordnung.12/(1)^2(6)^2/group.1705");
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, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ]
] ], size := 12 )
gap> P8 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.12/(1)^2(6)^2/words.group.1705"]);
gap> Append(GROUPS,[P8]);
gap> R := CaratReadBravaisFile("ordnung.12/(1)^2(6)^2/group.1706");
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, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ]
], size := 12 )
gap> P9 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.12/(1)^2(6)^2/words.group.1706"]);
gap> Append(GROUPS,[P9]);
gap> R := CaratReadBravaisFile("ordnung.12/(1)^2(6)^2/group.1707");
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, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 1 ] ] ]
, size := 12 )
gap> P10 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.12/(1)^2(6)^2/words.group.1707"]);
gap> Append(GROUPS,[P10]);
gap> R := CaratReadBravaisFile("ordnung.12/(1)^3(3)^1(6)^1(54)^1/group.1708");
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, -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 := 12 )
gap> P11 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.12/(1)^3(3)^1(6)^1(54)^1/words.group.1708"]);
gap> Append(GROUPS,[P11]);
gap> R := CaratReadBravaisFile("ordnung.12/(1)^3(3)^1(6)^1(54)^1/group.1709");
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 ] ],
[ [ 0, 1, 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 := 12 )
gap> P12 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.12/(1)^3(3)^1(6)^1(54)^1/words.group.1709"]);
gap> Append(GROUPS,[P12]);
gap> R := CaratReadBravaisFile("ordnung.12/(1)^3(3)^1(6)^1(54)^1/group.1710");
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, 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 := 12 )
gap> P13 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.12/(1)^3(3)^1(6)^1(54)^1/words.group.1710"]);
gap> Append(GROUPS,[P13]);
gap> R := CaratReadBravaisFile("ordnung.12/(1)^3(3)^1(6)^1(54)^1/group.1711");
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 ] ],
[ [ 0, -1, 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 := 12 )
gap> P14 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.12/(1)^3(3)^1(6)^1(54)^1/words.group.1711"]);
gap> Append(GROUPS,[P14]);
gap> R := CaratReadBravaisFile("ordnung.12/(1)^3(3)^1(6)^2/group.1712");
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, 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 := 12 )
gap> P15 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.12/(1)^3(3)^1(6)^2/words.group.1712"]);
gap> Append(GROUPS,[P15]);
gap> R := CaratReadBravaisFile("ordnung.12/(1)^3(3)^1(6)^2/group.1713");
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, -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 := 12 )
gap> P16 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.12/(1)^3(3)^1(6)^2/words.group.1713"]);
gap> Append(GROUPS,[P16]);
gap> R := CaratReadBravaisFile("ordnung.12/(1)^3(3)^1(6)^2/group.1714");
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 ] ],
[ [ 0, 1, 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 := 12 )
gap> P17 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.12/(1)^3(3)^1(6)^2/words.group.1714"]);
gap> Append(GROUPS,[P17]);
gap> R := CaratReadBravaisFile("ordnung.12/(3)^2(6)^2/group.1715");
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, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], [ 0, 0, 0, 0, 0, 1 ]
] ], size := 12 )
gap> P18 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.12/(3)^2(6)^2/words.group.1715"]);
gap> Append(GROUPS,[P18]);
gap> R := CaratReadBravaisFile("ordnung.24/(1)^2(3)^2(6)^1(18)^1/group.1716");
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, 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> P19 := Group(R.generators);
<matrix group with 3 generators>
gap> Append(names,["ordnung.24/(1)^2(3)^2(6)^1(18)^1/words.group.1716"]);
gap> Append(GROUPS,[P19]);
gap> R := CaratReadBravaisFile("ordnung.24/(1)^2(6)^2/group.1717");
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, 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> P20 := Group(R.generators);
<matrix group with 3 generators>
gap> Append(names,["ordnung.24/(1)^2(6)^2/words.group.1717"]);
gap> Append(GROUPS,[P20]);
gap> R := CaratReadBravaisFile("ordnung.24/(1)^3(3)^1(6)^1(54)^1/group.1718");
rec(
generators := [ [ [ 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 ] ],
[ [ -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, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ]
], size := 24 )
gap> P21 := Group(R.generators);
<matrix group with 3 generators>
gap> Append(names,["ordnung.24/(1)^3(3)^1(6)^1(54)^1/words.group.1718"]);
gap> Append(GROUPS,[P21]);
gap> R := CaratReadBravaisFile("ordnung.24/(1)^3(3)^1(6)^2/group.1719");
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 ] ],
[ [ 0, -1, 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 := 24 )
gap> P22 := Group(R.generators);
<matrix group with 3 generators>
gap> Append(names,["ordnung.24/(1)^3(3)^1(6)^2/words.group.1719"]);
gap> Append(GROUPS,[P22]);
gap> R := CaratReadBravaisFile("ordnung.24/(1)^3(3)^1(6)^2/group.1720");
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, 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> P23 := Group(R.generators);
<matrix group with 3 generators>
gap> Append(names,["ordnung.24/(1)^3(3)^1(6)^2/words.group.1720"]);
gap> Append(GROUPS,[P23]);
gap> R := CaratReadBravaisFile("ordnung.24/(1)^3(3)^1(6)^2/group.1721");
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, 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> P24 := Group(R.generators);
<matrix group with 3 generators>
gap> Append(names,["ordnung.24/(1)^3(3)^1(6)^2/words.group.1721"]);
gap> Append(GROUPS,[P24]);
gap> R := CaratReadBravaisFile("ordnung.24/(1)^3(3)^1(6)^2/group.1722");
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, 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> P25 := Group(R.generators);
<matrix group with 3 generators>
gap> Append(names,["ordnung.24/(1)^3(3)^1(6)^2/words.group.1722"]);
gap> Append(GROUPS,[P25]);
gap> R := CaratReadBravaisFile("ordnung.24/(1)^3(3)^1(6)^2/group.1723");
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, -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> P26 := Group(R.generators);
<matrix group with 3 generators>
gap> Append(names,["ordnung.24/(1)^3(3)^1(6)^2/words.group.1723"]);
gap> Append(GROUPS,[P26]);
gap> R := CaratReadBravaisFile("ordnung.24/(1)^3(3)^1(6)^2/group.1724");
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, 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> P27 := Group(R.generators);
<matrix group with 3 generators>
gap> Append(names,["ordnung.24/(1)^3(3)^1(6)^2/words.group.1724"]);
gap> Append(GROUPS,[P27]);
gap> R := CaratReadBravaisFile("ordnung.24/(1)^3(3)^1(6)^2/group.1725");
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, -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> P28 := Group(R.generators);
<matrix group with 3 generators>
gap> Append(names,["ordnung.24/(1)^3(3)^1(6)^2/words.group.1725"]);
gap> Append(GROUPS,[P28]);
gap> R := CaratReadBravaisFile("ordnung.48/(1)^3(3)^1(6)^2/group.1726");
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, 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 := 48 )
gap> P29 := Group(R.generators);
<matrix group with 4 generators>
gap> Append(names,["ordnung.48/(1)^3(3)^1(6)^2/words.group.1726"]);
gap> Append(GROUPS,[P29]);
gap> R := CaratReadBravaisFile("ordnung.6/(1)^2(3)^2(18)^1(54)^1/min.312");
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, 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 := 6 )
gap> P30 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.6/(1)^2(3)^2(18)^1(54)^1/words.min.312"]);
gap> Append(GROUPS,[P30]);
gap> R := CaratReadBravaisFile("ordnung.6/(1)^2(3)^2(18)^1(54)^1/min.313");
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, 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 := 6 )
gap> P31 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.6/(1)^2(3)^2(18)^1(54)^1/words.min.313"]);
gap> Append(GROUPS,[P31]);
gap> R := CaratReadBravaisFile("ordnung.6/(1)^2(6)^1(54)^1/min.314");
rec(
generators := [ [ [ 0, 1, 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 := 6 )
gap> P32 := Group(R.generators);
<matrix group with 1 generators>
gap> Append(names,["ordnung.6/(1)^2(6)^1(54)^1/words.min.314"]);
gap> Append(GROUPS,[P32]);
gap> R := CaratReadBravaisFile("ordnung.6/(1)^2(6)^1(54)^1/min.315");
rec(
generators := [ [ [ 0, -1, 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 := 6 )
gap> P33 := Group(R.generators);
<matrix group with 1 generators>
gap> Append(names,["ordnung.6/(1)^2(6)^1(54)^1/words.min.315"]);
gap> Append(GROUPS,[P33]);
gap> R := CaratReadBravaisFile("ordnung.6/(3)^2(6)^2/min.316");
rec(
generators := [ [ [ 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 := 6 )
gap> P34 := Group(R.generators);
<matrix group with 1 generators>
gap> Append(names,["ordnung.6/(3)^2(6)^2/words.min.316"]);
gap> Append(GROUPS,[P34]);
gap> R := CaratReadBravaisFile("ordnung.6/(3)^2(6)^2/min.317");
rec(
generators := [ [ [ -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 := 6 )
gap> P35 := Group(R.generators);
<matrix group with 1 generators>
gap> Append(names,["ordnung.6/(3)^2(6)^2/words.min.317"]);
gap> Append(GROUPS,[P35]);
gap> Print(GROUPS,"\n");
[ 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, -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 ] ],
[ [ 0, -1, 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, 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, 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 ] ],
[ [ 0, 1, 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, -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, 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, 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, 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, -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, 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, 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, -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 ]
],
[ [ 0, 1, 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, -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, 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 ] ],
[ [ 0, -1, 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, 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, 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, -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 ] ]
,
[ [ 0, 1, 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 ], [ 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, 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, -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, -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, 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 ] ],
[ [ -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, 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 ] ],
[ [ 0, -1, 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, 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, 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, -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, 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, 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, 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, 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 ] ],
[ [ -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([ [ [ 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, 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, 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, -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, 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, -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, 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.12/(1)^2(3)^2(18)^1(54)^1/words.group.1698",
"ordnung.12/(1)^2(3)^2(6)^1(18)^1/words.group.1699",
"ordnung.12/(1)^2(3)^2(6)^1(18)^1/words.group.1700",
"ordnung.12/(1)^2(3)^2(6)^1(18)^1/words.group.1701",
"ordnung.12/(1)^2(3)^2(6)^1(18)^1/words.group.1702",
"ordnung.12/(1)^2(6)^1(54)^1/words.group.1703",
"ordnung.12/(1)^2(6)^2/words.group.1704",
"ordnung.12/(1)^2(6)^2/words.group.1705",
"ordnung.12/(1)^2(6)^2/words.group.1706",
"ordnung.12/(1)^2(6)^2/words.group.1707",
"ordnung.12/(1)^3(3)^1(6)^1(54)^1/words.group.1708",
"ordnung.12/(1)^3(3)^1(6)^1(54)^1/words.group.1709",
"ordnung.12/(1)^3(3)^1(6)^1(54)^1/words.group.1710",
"ordnung.12/(1)^3(3)^1(6)^1(54)^1/words.group.1711",
"ordnung.12/(1)^3(3)^1(6)^2/words.group.1712",
"ordnung.12/(1)^3(3)^1(6)^2/words.group.1713",
"ordnung.12/(1)^3(3)^1(6)^2/words.group.1714",
"ordnung.12/(3)^2(6)^2/words.group.1715",
"ordnung.24/(1)^2(3)^2(6)^1(18)^1/words.group.1716",
"ordnung.24/(1)^2(6)^2/words.group.1717",
"ordnung.24/(1)^3(3)^1(6)^1(54)^1/words.group.1718",
"ordnung.24/(1)^3(3)^1(6)^2/words.group.1719",
"ordnung.24/(1)^3(3)^1(6)^2/words.group.1720",
"ordnung.24/(1)^3(3)^1(6)^2/words.group.1721",
"ordnung.24/(1)^3(3)^1(6)^2/words.group.1722",
"ordnung.24/(1)^3(3)^1(6)^2/words.group.1723",
"ordnung.24/(1)^3(3)^1(6)^2/words.group.1724",
"ordnung.24/(1)^3(3)^1(6)^2/words.group.1725",
"ordnung.48/(1)^3(3)^1(6)^2/words.group.1726",
"ordnung.6/(1)^2(3)^2(18)^1(54)^1/words.min.312",
"ordnung.6/(1)^2(3)^2(18)^1(54)^1/words.min.313",
"ordnung.6/(1)^2(6)^1(54)^1/words.min.314",
"ordnung.6/(1)^2(6)^1(54)^1/words.min.315",
"ordnung.6/(3)^2(6)^2/words.min.316", "ordnung.6/(3)^2(6)^2/words.min.317" ]
gap> Size(GROUPS);
35
gap> Size(names);
35
gap> Read("../../TGROUPS.GAP");
gap> for i in [1..Size(GROUPS)] do
> SubgroupWords(GROUPS[i], names[i]);
> od;
[ x1*x2^3, x2^2 ]
[ x1, x2^2 ]
[ x2^3, x2^2 ]
[ x1*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 ]
[ x1*x2^3, x2^2 ]
[ x2^3, x1 ]
[ x1*x2^3, x2^2 ]
[ x1, x2^2 ]
[ x2^3, x2^2 ]
[ x1*x2^3, x1 ]
[ x1*x2^3, x2^2 ]
[ x1, x2^2 ]
[ x2^3, x2^2 ]
[ x1*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 ]
[ x1*x2^3, x2^2 ]
[ x2^3, x1 ]
[ x2^3, x2^4 ]
[ x1, x2^4 ]
[ x1*x2^3, x2^4 ]
[ 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 ]
[ x1*x2^3, x2^2 ]
[ x2^3, x1 ]
[ x1*x2^3, x2^2 ]
[ x1, x2^2 ]
[ x2^3, x2^2 ]
[ x1*x2^3, x1 ]
[ x1*x2^3, x2^2 ]
[ x1, x2^2 ]
[ x2^3, x2^2 ]
[ x1*x2^3, x1 ]
[ 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 ]
[ x1*x2^3, x2^2 ]
[ x2^3, x1 ]
[ x1*x2^3, x2^2 ]
[ x1, x2^2 ]
[ x2^3, x2^2 ]
[ x1*x2^3, x1 ]
[ x1*x2^3, x2^2 ]
[ x1, x2^2 ]
[ x2^3, x2^2 ]
[ x1*x2^3, x1 ]
[ x2^3, x2^4 ]
[ x1, x2^4 ]
[ x1*x2^3, x2^4 ]
[ x2^3, x1 ]
[ x1*x3^3, x2, x3^2 ]
[ x1*x3^3, x1, x3^2 ]
[ x1*x3^3, x1*x2, x3^2 ]
[ x2, x1, x3^2 ]
[ x3^3, x2, x3^2 ]
[ x1*x2*x3^3, x1, x3^2 ]
[ x3^3, x1*x2, x3^2 ]
[ x1*x3^3, x2, x1 ]
[ x3^3, x2, x3^4 ]
[ x3^3, x1, x3^4 ]
[ x3^3, x1*x2, x3^4 ]
[ x2, x1, x3^4 ]
[ x1*x3^3, x2, x3^4 ]
[ x2*x3^3, x1, x3^4 ]
[ x1*x3^3, x1*x2, x3^4 ]
[ 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, 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 ]
[ x1*x3^3, x2, x3^2 ]
[ x1*x3^3, x1, x3^2 ]
[ x1*x3^3, x1*x2, x3^2 ]
[ x2, x1, x3^2 ]
[ x3^3, x2, x3^2 ]
[ x1*x2*x3^3, x1, x3^2 ]
[ x3^3, x1*x2, x3^2 ]
[ x1*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, 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, 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, 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, x1*x3, x2, x4^2 ]
[ x4^3, x1*x3, x1, x4^2 ]
[ x4^3, x1*x3, x1*x2, x4^2 ]
[ x4^3, x2, x1, x4^2 ]
[ x4^3, x3, x2, x4^2 ]
[ x4^3, x1*x2*x3, x1, x4^2 ]
[ x4^3, x3, x1*x2, x4^2 ]
[ x1*x3, x2, x1, x4^2 ]
[ x1*x4^3, x1*x3, x2, x4^2 ]
[ x2*x4^3, x1*x3, x1, x4^2 ]
[ x1*x4^3, x1*x3, x1*x2, x4^2 ]
[ x1*x3*x4^3, x2, x1, x4^2 ]
[ x1*x4^3, x3, x2, x4^2 ]
[ x2*x4^3, x1*x2*x3, x1, x4^2 ]
[ x1*x4^3, x3, x1*x2, x4^2 ]
[ x4^3, x1*x3, x2, x1 ]
[ x1*x2*x1 ]
[ x1 ]
[ x1*x2*x1 ]
[ x1 ]
[ x1^3 ]
[ x1^2 ]
[ x1^3 ]
[ x1^4 ]
[ x1^3 ]
[ x1^4 ]
[ x1^3 ]
[ x1^4 ]
gap> LogTo();