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.16/(2)^1(4)^4(8)^1/min.196");
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 ] ]
,
[ [ -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 ]
] ], size := 16 )
gap> P1 := Group(R.generators);
<matrix group with 4 generators>
gap> Append(names,["ordnung.16/(2)^1(4)^4(8)^1/words.min.196"]);
gap> Append(GROUPS,[P1]);
gap> R := CaratReadBravaisFile("ordnung.16/(2)^1(4)^4(8)^1/min.197");
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 ] ],
[ [ 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 ] ]
], size := 16 )
gap> P2 := Group(R.generators);
<matrix group with 4 generators>
gap> Append(names,["ordnung.16/(2)^1(4)^4(8)^1/words.min.197"]);
gap> Append(GROUPS,[P2]);
gap> R := CaratReadBravaisFile("ordnung.16/(2)^2(4)^2(8)^2/group.1070");
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 ] ],
[ [ 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 ] ]
], size := 16 )
gap> P3 := Group(R.generators);
<matrix group with 4 generators>
gap> Append(names,["ordnung.16/(2)^2(4)^2(8)^2/words.group.1070"]);
gap> Append(GROUPS,[P3]);
gap> R := CaratReadBravaisFile("ordnung.16/(2)^2(4)^2(8)^2/group.1071");
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 ] ],
[ [ 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 ] ]
], size := 16 )
gap> P4 := Group(R.generators);
<matrix group with 4 generators>
gap> Append(names,["ordnung.16/(2)^2(4)^2(8)^2/words.group.1071"]);
gap> Append(GROUPS,[P4]);
gap> R := CaratReadBravaisFile("ordnung.16/(2)^2(4)^2(8)^2/group.1072");
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 ] ],
[ [ -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 ]
] ], size := 16 )
gap> P5 := Group(R.generators);
<matrix group with 4 generators>
gap> Append(names,["ordnung.16/(2)^2(4)^2(8)^2/words.group.1072"]);
gap> Append(GROUPS,[P5]);
gap> R := CaratReadBravaisFile("ordnung.16/(2)^2(4)^2(8)^2/group.1073");
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 ] ],
[ [ 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 ] ]
], size := 16 )
gap> P6 := Group(R.generators);
<matrix group with 4 generators>
gap> Append(names,["ordnung.16/(2)^2(4)^2(8)^2/words.group.1073"]);
gap> Append(GROUPS,[P6]);
gap> R := CaratReadBravaisFile("ordnung.16/(2)^2(8)^4/group.1074");
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 ] ]
,
[ [ 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 ]
] ], size := 16 )
gap> P7 := Group(R.generators);
<matrix group with 4 generators>
gap> Append(names,["ordnung.16/(2)^2(8)^4/words.group.1074"]);
gap> Append(GROUPS,[P7]);
gap> R := CaratReadBravaisFile("ordnung.32/(2)^1(4)^4(8)^1/group.1075");
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 ] ],
[ [ -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, 0, 0, 0, 0, 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 := 32 )
gap> P8 := Group(R.generators);
<matrix group with 5 generators>
gap> Append(names,["ordnung.32/(2)^1(4)^4(8)^1/words.group.1075"]);
gap> Append(GROUPS,[P8]);
gap> R := CaratReadBravaisFile("ordnung.32/(2)^2(4)^2(8)^2/group.1076");
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 ] ],
[ [ -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, 0, 0, 0, 0, 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 := 32 )
gap> P9 := Group(R.generators);
<matrix group with 5 generators>
gap> Append(names,["ordnung.32/(2)^2(4)^2(8)^2/words.group.1076"]);
gap> Append(GROUPS,[P9]);
gap> R := CaratReadBravaisFile("ordnung.32/(2)^2(4)^4/group.1077");
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 ] ],
[ [ -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, 0, 0, 0, 0, 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 := 32 )
gap> P10 := Group(R.generators);
<matrix group with 5 generators>
gap> Append(names,["ordnung.32/(2)^2(4)^4/words.group.1077"]);
gap> Append(GROUPS,[P10]);
gap> R := CaratReadBravaisFile("ordnung.32/(2)^2(4)^4/group.1078");
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 ] ],
[ [ 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, 0, 0, 0, 0, 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 := 32 )
gap> P11 := Group(R.generators);
<matrix group with 5 generators>
gap> Append(names,["ordnung.32/(2)^2(4)^4/words.group.1078"]);
gap> Append(GROUPS,[P11]);
gap> R := CaratReadBravaisFile("ordnung.32/(2)^2(4)^4/group.1079");
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 ] ],
[ [ -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, 0, 0, 0, 0, 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 := 32 )
gap> P12 := Group(R.generators);
<matrix group with 5 generators>
gap> Append(names,["ordnung.32/(2)^2(4)^4/words.group.1079"]);
gap> Append(GROUPS,[P12]);
gap> R := CaratReadBravaisFile("ordnung.64/(2)^2(4)^4/group.1080");
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 ] ],
[ [ 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, 0, 0, 0, 0, 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 ] ]
], size := 64 )
gap> P13 := Group(R.generators);
<matrix group with 6 generators>
gap> Append(names,["ordnung.64/(2)^2(4)^4/words.group.1080"]);
gap> Append(GROUPS,[P13]);
gap> R := CaratReadBravaisFile("ordnung.8/(2)^2(8)^4/min.198");
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 ] ]
,
[ [ -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 ] ]
], size := 8 )
gap> P14 := Group(R.generators);
<matrix group with 3 generators>
gap> Append(names,["ordnung.8/(2)^2(8)^4/words.min.198"]);
gap> Append(GROUPS,[P14]);
gap> R := CaratReadBravaisFile("ordnung.8/(2)^2(8)^4/min.199");
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 ] ]
,
[ [ -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 ] ]
], size := 8 )
gap> P15 := Group(R.generators);
<matrix group with 3 generators>
gap> Append(names,["ordnung.8/(2)^2(8)^4/words.min.199"]);
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 ] ],
[ [ 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, 0, 0, 0, 0, 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([ [ [ 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, 0, 0, 0, 0, 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 ] ]
]),
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 ] ],
[ [ 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 ] ]
]),
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 ] ],
[ [ 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 ] ]
]),
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 ] ],
[ [ -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 ]
] ]),
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 ] ],
[ [ 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 ] ]
]),
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 ] ]
,
[ [ 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 ]
] ]),
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 ] ],
[ [ -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, 0, 0, 0, 0, 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([ [ [ 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, 0, 0, 0, 0, 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, 0, 0, 0, 0, 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([ [ [ 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, 0, 0, 0, 0, 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, 0, 0, 0, 0, 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([ [ [ 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, 0, 0, 0, 0, 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, 0, 0, 0, 0, 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([ [ [ 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, 0, 0, 0, 0, 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, 0, 0, 0, 0, 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([ [ [ 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, 0, 0, 0, 0, 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, 0, 0, 0, 0, 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 ] ]
]),
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 ] ]
,
[ [ -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 ] ]
]),
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 ] ]
,
[ [ -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 ] ]
]) ]
gap> Print(names,"\n");
[ "ordnung.16/(2)^1(4)^4(8)^1/words.min.196",
"ordnung.16/(2)^1(4)^4(8)^1/words.min.197",
"ordnung.16/(2)^2(4)^2(8)^2/words.group.1070",
"ordnung.16/(2)^2(4)^2(8)^2/words.group.1071",
"ordnung.16/(2)^2(4)^2(8)^2/words.group.1072",
"ordnung.16/(2)^2(4)^2(8)^2/words.group.1073",
"ordnung.16/(2)^2(8)^4/words.group.1074",
"ordnung.32/(2)^1(4)^4(8)^1/words.group.1075",
"ordnung.32/(2)^2(4)^2(8)^2/words.group.1076",
"ordnung.32/(2)^2(4)^4/words.group.1077",
"ordnung.32/(2)^2(4)^4/words.group.1078",
"ordnung.32/(2)^2(4)^4/words.group.1079",
"ordnung.64/(2)^2(4)^4/words.group.1080",
"ordnung.8/(2)^2(8)^4/words.min.198", "ordnung.8/(2)^2(8)^4/words.min.199" ]
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;
[ x4, x1*x3, x1*x2 ]
[ x4, x1*x3, x1 ]
[ x4, x1*x3, x2 ]
[ x4, x1*x2, x1 ]
[ x4, x3, x1*x2 ]
[ x4, x2*x3, x1 ]
[ x4, x3, x2 ]
[ x1*x3, x1*x2, x1 ]
[ x1*x4, x1*x3, x1*x2 ]
[ x1*x2*x4, x1*x3, x1 ]
[ x1*x4, x1*x3, x2 ]
[ x1*x3*x4, x1*x2, x1 ]
[ x1*x4, x3, x1*x2 ]
[ x1*x2*x4, x2*x3, x1 ]
[ x1*x4, x3, x2 ]
[ x1*x2*x3*x4, x3, x2 ]
[ x1*x2*x3*x4, x3, x1 ]
[ x1*x2*x3*x4, x3, x1*x2 ]
[ x1*x2*x3*x4, x2, x1 ]
[ x1*x2*x3*x4, x1*x3, x2 ]
[ x1*x2*x3*x4, x2*x3, x1 ]
[ x1*x2*x3*x4, x1*x3, x1*x2 ]
[ x3, x2, x1 ]
[ x2*x3*x4, x3, x2 ]
[ x1*x3*x4, x3, x1 ]
[ x2*x3*x4, x3, x1*x2 ]
[ x1*x2*x4, x2, x1 ]
[ x2*x3*x4, x1*x3, x2 ]
[ x1*x3*x4, x2*x3, x1 ]
[ x2*x3*x4, x1*x3, x1*x2 ]
[ x4, x3, x2 ]
[ x4, x3, x1 ]
[ x4, x3, x1*x2 ]
[ x4, x2, x1 ]
[ x4, x1*x3, x2 ]
[ x4, x2*x3, x1 ]
[ x4, x1*x3, x1*x2 ]
[ x3, x2, x1 ]
[ x1*x4, x3, x2 ]
[ x2*x4, x3, x1 ]
[ x1*x4, x3, x1*x2 ]
[ x3*x4, x2, x1 ]
[ x1*x4, x1*x3, x2 ]
[ x2*x4, x2*x3, x1 ]
[ x1*x4, x1*x3, x1*x2 ]
[ x4, x3, x1*x2 ]
[ x4, x3, x1 ]
[ x4, x3, x2 ]
[ x4, x1*x2, x1 ]
[ x4, x1*x3, x1*x2 ]
[ x4, x1*x2*x3, x1 ]
[ x4, x1*x3, x2 ]
[ x3, x1*x2, x1 ]
[ x1*x4, x3, x1*x2 ]
[ x1*x2*x4, x3, x1 ]
[ x1*x4, x3, x2 ]
[ x3*x4, x1*x2, x1 ]
[ x1*x4, x1*x3, x1*x2 ]
[ x1*x2*x4, x1*x2*x3, x1 ]
[ x1*x4, x1*x3, x2 ]
[ x1*x2*x4, x3, x2 ]
[ x1*x2*x4, x3, x1 ]
[ x1*x2*x4, x3, x1*x2 ]
[ x1*x2*x4, x2, x1 ]
[ x1*x2*x4, x1*x3, x2 ]
[ x1*x2*x4, x2*x3, x1 ]
[ x1*x2*x4, x1*x3, x1*x2 ]
[ x3, x2, x1 ]
[ x2*x4, x3, x2 ]
[ x1*x4, x3, x1 ]
[ x2*x4, x3, x1*x2 ]
[ x1*x2*x3*x4, x2, x1 ]
[ x2*x4, x1*x3, x2 ]
[ x1*x4, x2*x3, x1 ]
[ x2*x4, x1*x3, x1*x2 ]
[ x4, x1*x3, x1*x2 ]
[ x4, x1*x3, x1 ]
[ x4, x1*x3, x2 ]
[ x4, x1*x2, x1 ]
[ x4, x3, x1*x2 ]
[ x4, x2*x3, x1 ]
[ x4, x3, x2 ]
[ x1*x3, x1*x2, x1 ]
[ x1*x4, x1*x3, x1*x2 ]
[ x1*x2*x4, x1*x3, x1 ]
[ x1*x4, x1*x3, x2 ]
[ x1*x3*x4, x1*x2, x1 ]
[ x1*x4, x3, x1*x2 ]
[ x1*x2*x4, x2*x3, x1 ]
[ x1*x4, x3, x2 ]
[ x3*x4, x1*x2*x3, x2 ]
[ x3*x4, x1*x2*x3, x1 ]
[ x3*x4, x1*x2*x3, x1*x2 ]
[ x3*x4, x2, x1 ]
[ x3*x4, x2*x3, x2 ]
[ x3*x4, x1*x3, x1 ]
[ x3*x4, x2*x3, x1*x2 ]
[ x1*x2*x3, x2, x1 ]
[ x1*x3*x4, x1*x2*x3, x2 ]
[ x2*x3*x4, x1*x2*x3, x1 ]
[ x1*x3*x4, x1*x2*x3, x1*x2 ]
[ x1*x2*x4, x2, x1 ]
[ x1*x3*x4, x2*x3, x2 ]
[ x2*x3*x4, x1*x3, x1 ]
[ x1*x3*x4, x2*x3, x1*x2 ]
[ x1*x5, x4, x3, x2 ]
[ x1*x5, x4, x3, x1 ]
[ x1*x5, x4, x3, x1*x2 ]
[ x1*x5, x4, x2, x1 ]
[ x1*x5, x4, x1*x3, x2 ]
[ x1*x5, x4, x2*x3, x1 ]
[ x1*x5, x4, x1*x3, x1*x2 ]
[ x1*x5, x3, x2, x1 ]
[ x1*x5, x1*x4, x3, x2 ]
[ x1*x5, x2*x4, x3, x1 ]
[ x1*x5, x1*x4, x3, x1*x2 ]
[ x1*x5, x3*x4, x2, x1 ]
[ x1*x5, x1*x4, x1*x3, x2 ]
[ x1*x5, x2*x4, x2*x3, x1 ]
[ x1*x5, x1*x4, x1*x3, x1*x2 ]
[ x4, x3, x2, x1 ]
[ x5, x4, x3, x2 ]
[ x1*x2*x5, x4, x3, x1 ]
[ x5, x4, x3, x1*x2 ]
[ x1*x3*x5, x4, x2, x1 ]
[ x5, x4, x1*x3, x2 ]
[ x1*x2*x5, x4, x2*x3, x1 ]
[ x5, x4, x1*x3, x1*x2 ]
[ x1*x4*x5, x3, x2, x1 ]
[ x5, x1*x4, x3, x2 ]
[ x1*x2*x5, x2*x4, x3, x1 ]
[ x5, x1*x4, x3, x1*x2 ]
[ x1*x3*x5, x3*x4, x2, x1 ]
[ x5, x1*x4, x1*x3, x2 ]
[ x1*x2*x5, x2*x4, x2*x3, x1 ]
[ x5, x1*x4, x1*x3, x1*x2 ]
[ x2*x5, x4, x1*x3, x2 ]
[ x2*x5, x4, x1*x3, x1 ]
[ x2*x5, x4, x1*x3, x1*x2 ]
[ x2*x5, x4, x2, x1 ]
[ x2*x5, x4, x3, x2 ]
[ x2*x5, x4, x1*x2*x3, x1 ]
[ x2*x5, x4, x3, x1*x2 ]
[ x2*x5, x1*x3, x2, x1 ]
[ x2*x5, x1*x4, x1*x3, x2 ]
[ x2*x5, x2*x4, x1*x3, x1 ]
[ x2*x5, x1*x4, x1*x3, x1*x2 ]
[ x2*x5, x1*x3*x4, x2, x1 ]
[ x2*x5, x1*x4, x3, x2 ]
[ x2*x5, x2*x4, x1*x2*x3, x1 ]
[ x2*x5, x1*x4, x3, x1*x2 ]
[ x4, x1*x3, x2, x1 ]
[ x1*x2*x5, x4, x1*x3, x2 ]
[ x5, x4, x1*x3, x1 ]
[ x1*x2*x5, x4, x1*x3, x1*x2 ]
[ x1*x2*x3*x5, x4, x2, x1 ]
[ x1*x2*x5, x4, x3, x2 ]
[ x5, x4, x1*x2*x3, x1 ]
[ x1*x2*x5, x4, x3, x1*x2 ]
[ x2*x4*x5, x1*x3, x2, x1 ]
[ x1*x2*x5, x1*x4, x1*x3, x2 ]
[ x5, x2*x4, x1*x3, x1 ]
[ x1*x2*x5, x1*x4, x1*x3, x1*x2 ]
[ x1*x2*x3*x5, x1*x3*x4, x2, x1 ]
[ x1*x2*x5, x1*x4, x3, x2 ]
[ x5, x2*x4, x1*x2*x3, x1 ]
[ x1*x2*x5, x1*x4, x3, x1*x2 ]
[ x1*x5, x4, x3, x2 ]
[ x1*x5, x4, x3, x1 ]
[ x1*x5, x4, x3, x1*x2 ]
[ x1*x5, x4, x2, x1 ]
[ x1*x5, x4, x1*x3, x2 ]
[ x1*x5, x4, x2*x3, x1 ]
[ x1*x5, x4, x1*x3, x1*x2 ]
[ x1*x5, x3, x2, x1 ]
[ x1*x5, x1*x4, x3, x2 ]
[ x1*x5, x2*x4, x3, x1 ]
[ x1*x5, x1*x4, x3, x1*x2 ]
[ x1*x5, x3*x4, x2, x1 ]
[ x1*x5, x1*x4, x1*x3, x2 ]
[ x1*x5, x2*x4, x2*x3, x1 ]
[ x1*x5, x1*x4, x1*x3, x1*x2 ]
[ x4, x3, x2, x1 ]
[ x5, x4, x3, x2 ]
[ x1*x2*x5, x4, x3, x1 ]
[ x5, x4, x3, x1*x2 ]
[ x1*x3*x5, x4, x2, x1 ]
[ x5, x4, x1*x3, x2 ]
[ x1*x2*x5, x4, x2*x3, x1 ]
[ x5, x4, x1*x3, x1*x2 ]
[ x1*x4*x5, x3, x2, x1 ]
[ x5, x1*x4, x3, x2 ]
[ x1*x2*x5, x2*x4, x3, x1 ]
[ x5, x1*x4, x3, x1*x2 ]
[ x1*x3*x5, x3*x4, x2, x1 ]
[ x5, x1*x4, x1*x3, x2 ]
[ x1*x2*x5, x2*x4, x2*x3, x1 ]
[ x5, x1*x4, x1*x3, x1*x2 ]
[ x1*x5, x4, x3, x2 ]
[ x1*x5, x4, x3, x1 ]
[ x1*x5, x4, x3, x1*x2 ]
[ x1*x5, x4, x2, x1 ]
[ x1*x5, x4, x1*x3, x2 ]
[ x1*x5, x4, x2*x3, x1 ]
[ x1*x5, x4, x1*x3, x1*x2 ]
[ x1*x5, x3, x2, x1 ]
[ x1*x5, x1*x4, x3, x2 ]
[ x1*x5, x2*x4, x3, x1 ]
[ x1*x5, x1*x4, x3, x1*x2 ]
[ x1*x5, x3*x4, x2, x1 ]
[ x1*x5, x1*x4, x1*x3, x2 ]
[ x1*x5, x2*x4, x2*x3, x1 ]
[ x1*x5, x1*x4, x1*x3, x1*x2 ]
[ x4, x3, x2, x1 ]
[ x5, x4, x3, x2 ]
[ x1*x2*x5, x4, x3, x1 ]
[ x5, x4, x3, x1*x2 ]
[ x1*x3*x5, x4, x2, x1 ]
[ x5, x4, x1*x3, x2 ]
[ x1*x2*x5, x4, x2*x3, x1 ]
[ x5, x4, x1*x3, x1*x2 ]
[ x1*x4*x5, x3, x2, x1 ]
[ x5, x1*x4, x3, x2 ]
[ x1*x2*x5, x2*x4, x3, x1 ]
[ x5, x1*x4, x3, x1*x2 ]
[ x1*x3*x5, x3*x4, x2, x1 ]
[ x5, x1*x4, x1*x3, x2 ]
[ x1*x2*x5, x2*x4, x2*x3, x1 ]
[ x5, x1*x4, x1*x3, x1*x2 ]
[ x5, x4, x3, x2 ]
[ x5, x4, x3, x1 ]
[ x5, x4, x3, x1*x2 ]
[ x5, x4, x2, x1 ]
[ x5, x4, x1*x3, x2 ]
[ x5, x4, x2*x3, x1 ]
[ x5, x4, x1*x3, x1*x2 ]
[ x5, x3, x2, x1 ]
[ x5, x1*x4, x3, x2 ]
[ x5, x2*x4, x3, x1 ]
[ x5, x1*x4, x3, x1*x2 ]
[ x5, x3*x4, x2, x1 ]
[ x5, x1*x4, x1*x3, x2 ]
[ x5, x2*x4, x2*x3, x1 ]
[ x5, x1*x4, x1*x3, x1*x2 ]
[ x4, x3, x2, x1 ]
[ x1*x5, x4, x3, x2 ]
[ x2*x5, x4, x3, x1 ]
[ x1*x5, x4, x3, x1*x2 ]
[ x3*x5, x4, x2, x1 ]
[ x1*x5, x4, x1*x3, x2 ]
[ x2*x5, x4, x2*x3, x1 ]
[ x1*x5, x4, x1*x3, x1*x2 ]
[ x4*x5, x3, x2, x1 ]
[ x1*x5, x1*x4, x3, x2 ]
[ x2*x5, x2*x4, x3, x1 ]
[ x1*x5, x1*x4, x3, x1*x2 ]
[ x3*x5, x3*x4, x2, x1 ]
[ x1*x5, x1*x4, x1*x3, x2 ]
[ x2*x5, x2*x4, x2*x3, x1 ]
[ x1*x5, x1*x4, x1*x3, x1*x2 ]
[ x4*x6, x3*x5, x4, x3, x2 ]
[ x4*x6, x3*x5, x4, x3, x1 ]
[ x4*x6, x3*x5, x4, x3, x1*x2 ]
[ x4*x6, x3*x5, x4, x2, x1 ]
[ x4*x6, x3*x5, x4, x1*x3, x2 ]
[ x4*x6, x3*x5, x4, x2*x3, x1 ]
[ x4*x6, x3*x5, x4, x1*x3, x1*x2 ]
[ x4*x6, x3*x5, x3, x2, x1 ]
[ x4*x6, x3*x5, x1*x4, x3, x2 ]
[ x4*x6, x3*x5, x2*x4, x3, x1 ]
[ x4*x6, x3*x5, x1*x4, x3, x1*x2 ]
[ x4*x6, x3*x5, x3*x4, x2, x1 ]
[ x4*x6, x3*x5, x1*x4, x1*x3, x2 ]
[ x4*x6, x3*x5, x2*x4, x2*x3, x1 ]
[ x4*x6, x3*x5, x1*x4, x1*x3, x1*x2 ]
[ x4*x6, x4, x3, x2, x1 ]
[ x4*x6, x1*x3*x5, x4, x3, x2 ]
[ x4*x6, x2*x3*x5, x4, x3, x1 ]
[ x4*x6, x1*x3*x5, x4, x3, x1*x2 ]
[ x4*x6, x5, x4, x2, x1 ]
[ x4*x6, x1*x3*x5, x4, x1*x3, x2 ]
[ x4*x6, x2*x3*x5, x4, x2*x3, x1 ]
[ x4*x6, x1*x3*x5, x4, x1*x3, x1*x2 ]
[ x4*x6, x3*x4*x5, x3, x2, x1 ]
[ x4*x6, x1*x3*x5, x1*x4, x3, x2 ]
[ x4*x6, x2*x3*x5, x2*x4, x3, x1 ]
[ x4*x6, x1*x3*x5, x1*x4, x3, x1*x2 ]
[ x4*x6, x5, x3*x4, x2, x1 ]
[ x4*x6, x1*x3*x5, x1*x4, x1*x3, x2 ]
[ x4*x6, x2*x3*x5, x2*x4, x2*x3, x1 ]
[ x4*x6, x1*x3*x5, x1*x4, x1*x3, x1*x2 ]
[ x3*x5, x4, x3, x2, x1 ]
[ x1*x4*x6, x3*x5, x4, x3, x2 ]
[ x2*x4*x6, x3*x5, x4, x3, x1 ]
[ x1*x4*x6, x3*x5, x4, x3, x1*x2 ]
[ x3*x4*x6, x3*x5, x4, x2, x1 ]
[ x1*x4*x6, x3*x5, x4, x1*x3, x2 ]
[ x2*x4*x6, x3*x5, x4, x2*x3, x1 ]
[ x1*x4*x6, x3*x5, x4, x1*x3, x1*x2 ]
[ x6, x3*x5, x3, x2, x1 ]
[ x1*x4*x6, x3*x5, x1*x4, x3, x2 ]
[ x2*x4*x6, x3*x5, x2*x4, x3, x1 ]
[ x1*x4*x6, x3*x5, x1*x4, x3, x1*x2 ]
[ x3*x4*x6, x3*x5, x3*x4, x2, x1 ]
[ x1*x4*x6, x3*x5, x1*x4, x1*x3, x2 ]
[ x2*x4*x6, x3*x5, x2*x4, x2*x3, x1 ]
[ x1*x4*x6, x3*x5, x1*x4, x1*x3, x1*x2 ]
[ x3*x4*x5*x6, x4, x3, x2, x1 ]
[ x1*x4*x6, x1*x3*x5, x4, x3, x2 ]
[ x2*x4*x6, x2*x3*x5, x4, x3, x1 ]
[ x1*x4*x6, x1*x3*x5, x4, x3, x1*x2 ]
[ x3*x4*x6, x5, x4, x2, x1 ]
[ x1*x4*x6, x1*x3*x5, x4, x1*x3, x2 ]
[ x2*x4*x6, x2*x3*x5, x4, x2*x3, x1 ]
[ x1*x4*x6, x1*x3*x5, x4, x1*x3, x1*x2 ]
[ x6, x3*x4*x5, x3, x2, x1 ]
[ x1*x4*x6, x1*x3*x5, x1*x4, x3, x2 ]
[ x2*x4*x6, x2*x3*x5, x2*x4, x3, x1 ]
[ x1*x4*x6, x1*x3*x5, x1*x4, x3, x1*x2 ]
[ x3*x4*x6, x5, x3*x4, x2, x1 ]
[ x1*x4*x6, x1*x3*x5, x1*x4, x1*x3, x2 ]
[ x2*x4*x6, x2*x3*x5, x2*x4, x2*x3, x1 ]
[ x1*x4*x6, x1*x3*x5, x1*x4, x1*x3, x1*x2 ]
[ x1*x3, x2 ]
[ x1*x3, x1 ]
[ x1*x3, x1*x2 ]
[ x2, x1 ]
[ x3, x2 ]
[ x1*x2*x3, x1 ]
[ x3, x1*x2 ]
[ x1*x2*x3, x1*x2 ]
[ x1*x2*x3, x1 ]
[ x1*x2*x3, x2 ]
[ x1*x2, x1 ]
[ x2*x3, x1*x2 ]
[ x3, x1 ]
[ x2*x3, x2 ]
gap> LogTo();