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(4)^1(12)^1/min.349");
rec(
generators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ -1, 1, 0, 0, 0, 0 ], [ 0, 0, 0,
1, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, -1 ],
[ 0, 0, -1, 0, 1, 0 ] ] ], size := 12 )
gap> P1 := Group(R.generators);
<matrix group with 1 generators>
gap> Append(names,["ordnung.12/(1)^2(4)^1(12)^1/words.min.349"]);
gap> Append(GROUPS,[P1]);
gap> R := CaratReadBravaisFile("ordnung.12/(1)^2(4)^1(12)^1/min.350");
rec(
generators := [ [ [ 0, -1, 0, 0, 0, 0 ], [ 1, -1, 0, 0, 0, 0 ], [ 0, 0, 0,
1, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, -1 ],
[ 0, 0, -1, 0, 1, 0 ] ] ], size := 12 )
gap> P2 := Group(R.generators);
<matrix group with 1 generators>
gap> Append(names,["ordnung.12/(1)^2(4)^1(12)^1/words.min.350"]);
gap> Append(GROUPS,[P2]);
gap> R := CaratReadBravaisFile("ordnung.12/(1)^4(12)^2/min.351");
rec(
generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 1, -1, 0, 0, 0, 0 ], [ 0, 0, 0,
1, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, -1 ],
[ 0, 0, -1, 0, 1, 0 ] ],
[ [ -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)^4(12)^2/words.min.351"]);
gap> Append(GROUPS,[P3]);
gap> R := CaratReadBravaisFile("ordnung.24/(1)^2(4)^1(12)^1/group.1903");
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, 0, -1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 1 ], [ 0, 0, 1, 0, -1, 0 ]
] ], size := 24 )
gap> P4 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.24/(1)^2(4)^1(12)^1/words.group.1903"]);
gap> Append(GROUPS,[P4]);
gap> R := CaratReadBravaisFile("ordnung.24/(1)^4(12)^2/group.1904");
rec(
generators := [ [ [ 1, 0, 0, 0, 0, 0 ], [ 1, -1, 0, 0, 0, 0 ], [ 0, 0, 0,
1, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, -1 ],
[ 0, 0, -1, 0, 1, 0 ] ],
[ [ 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 ] ] ]
, size := 24 )
gap> P5 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.24/(1)^4(12)^2/words.group.1904"]);
gap> Append(GROUPS,[P5]);
gap> R := CaratReadBravaisFile("ordnung.24/(1)^4(12)^2/group.1905");
rec(
generators := [ [ [ -1, 0, 0, 0, 0, 0 ], [ -1, 1, 0, 0, 0, 0 ], [ 0, 0, 0,
1, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, -1 ],
[ 0, 0, -1, 0, 1, 0 ] ],
[ [ 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 ] ] ]
, size := 24 )
gap> P6 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.24/(1)^4(12)^2/words.group.1905"]);
gap> Append(GROUPS,[P6]);
gap> R := CaratReadBravaisFile("ordnung.24/(1)^4(12)^2/group.1906");
rec(
generators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0,
-1, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0 ] ],
[ [ 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> P7 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.24/(1)^4(12)^2/words.group.1906"]);
gap> Append(GROUPS,[P7]);
gap> R := CaratReadBravaisFile("ordnung.48/(1)^4(12)^2/group.1907");
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 ], [ -1, 1, 0, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 1 ], [ 0, 0, 1, 0, -1, 0 ]
] ], size := 48 )
gap> P8 := Group(R.generators);
<matrix group with 3 generators>
gap> Append(names,["ordnung.48/(1)^4(12)^2/words.group.1907"]);
gap> Append(GROUPS,[P8]);
gap> Print(GROUPS,"\n");
[ Group(
[ [ [ 0, 1, 0, 0, 0, 0 ], [ -1, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ],
[ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, -1 ], [ 0, 0, -1, 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, 0, 0, 0 ], [ 0, 0, 0, 1, 0, -1 ],
[ 0, 0, -1, 0, 1, 0 ] ] ]),
Group([ [ [ 1, 0, 0, 0, 0, 0 ], [ 1, -1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ],
[ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, -1 ], [ 0, 0, -1, 0, 1, 0 ]
],
[ [ -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, 0, -1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 1 ], [ 0, 0, 1, 0, -1, 0 ]
] ]),
Group([ [ [ 1, 0, 0, 0, 0, 0 ], [ 1, -1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ],
[ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, -1 ], [ 0, 0, -1, 0, 1, 0 ]
],
[ [ 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 ] ]
]),
Group([ [ [ -1, 0, 0, 0, 0, 0 ], [ -1, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ]
, [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, -1 ],
[ 0, 0, -1, 0, 1, 0 ] ],
[ [ 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 ] ]
]),
Group([ [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ],
[ 0, 0, 0, 0, 0, 1 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ] ],
[ [ 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 ], [ -1, 1, 0, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 1 ], [ 0, 0, 1, 0, -1, 0 ]
] ]) ]
gap> Print(names,"\n");
[ "ordnung.12/(1)^2(4)^1(12)^1/words.min.349",
"ordnung.12/(1)^2(4)^1(12)^1/words.min.350",
"ordnung.12/(1)^4(12)^2/words.min.351",
"ordnung.24/(1)^2(4)^1(12)^1/words.group.1903",
"ordnung.24/(1)^4(12)^2/words.group.1904",
"ordnung.24/(1)^4(12)^2/words.group.1905",
"ordnung.24/(1)^4(12)^2/words.group.1906",
"ordnung.48/(1)^4(12)^2/words.group.1907" ]
gap> Size(GROUPS);
8
gap> Size(names);
8
gap> Read("../../TGROUPS.GAP");
gap> for i in [1..Size(GROUPS)] do
> SubgroupWords(GROUPS[i], names[i]);
> od;
[ x1^6, x1^9 ]
[ x1^8, x1^6 ]
[ x1^6, x1^3 ]
[ x1^8, x1^6 ]
[ x1^2, x1^3*x2*x1 ]
[ x2*x1, x1^2 ]
[ x2^3, x2^4, x2^6 ]
[ x1, x2^4, x2^6 ]
[ x1*x2^3, x2^4, x2^6 ]
[ x2^3, x1, x2^6 ]
[ x1^2*x2*x1*x2*x1*x2, x1^2, x1^3*x2*x1*x2 ]
[ x1, x1^2, x1^3*x2*x1*x2 ]
[ x1^3*x2*x1*x2*x1*x2, x1^2, x1^3*x2*x1*x2 ]
[ x1^2*x2*x1*x2*x1*x2, x1, x1^2 ]
[ x1^3*x2*x1*x2*x1*x2, x1^2, x1^3*x2*x1*x2 ]
[ x1, x1^2, x1^3*x2*x1*x2 ]
[ x2*x1*x2*x1*x2, x1^2, x1^3*x2*x1*x2 ]
[ x1^3*x2*x1*x2*x1*x2, x1, x1^2 ]
[ x1*x2^3, x1^2, x2^2 ]
[ x1, x1^2, x2^2 ]
[ x1^2*x2^3, x1^2, x2^2 ]
[ x1*x2^3, x1, x1^2 ]
[ x1*x3*x1*x3*x1*x3^3, x1*x2, x3^2, x1*x3*x1*x3^3 ]
[ x1*x3*x1*x3*x1*x3^3, x1, x3^2, x1*x3*x1*x3^3 ]
[ x1*x3*x1*x3*x1*x3^3, x2, x3^2, x1*x3*x1*x3^3 ]
[ x1*x2, x1, x3^2, x1*x3*x1*x3^3 ]
[ x3*x1*x3*x1*x3^3, x1*x2, x3^2, x1*x3*x1*x3^3 ]
[ x2*x3*x1*x3*x1*x3^3, x1, x3^2, x1*x3*x1*x3^3 ]
[ x3*x1*x3*x1*x3^3, x2, x3^2, x1*x3*x1*x3^3 ]
[ x1*x3*x1*x3*x1*x3^3, x1*x2, x1, x3^2 ]
gap> LogTo();