gap> RequirePackage("carat");
true
gap> names := [];
[  ]
gap> GROUPS := [];
[  ]
gap> R := CaratReadBravaisFile("ordnung.12/(2)^2(6)^1(18)^1/group.1613");
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, 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)^2(6)^1(18)^1/words.group.1613"]);
gap> Append(GROUPS,[P1]);
gap> R := CaratReadBravaisFile("ordnung.12/(2)^3(6)^1/group.1614");
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, 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/(2)^3(6)^1/words.group.1614"]);
gap> Append(GROUPS,[P2]);
gap> R := CaratReadBravaisFile("ordnung.12/(2)^3(6)^1/group.1615");
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, 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/(2)^3(6)^1/words.group.1615"]);
gap> Append(GROUPS,[P3]);
gap> R := CaratReadBravaisFile("ordnung.12/(2)^3(6)^1/group.1616");
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, 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/(2)^3(6)^1/words.group.1616"]);
gap> Append(GROUPS,[P4]);
gap> R := CaratReadBravaisFile("ordnung.24/(2)^3(6)^1/group.1617");
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, 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 3 generators>
gap> Append(names,["ordnung.24/(2)^3(6)^1/words.group.1617"]);
gap> Append(GROUPS,[P5]);
gap> R := CaratReadBravaisFile("ordnung.6/(2)^2(6)^1(18)^1/min.292");
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 ] ] ], size := 6 )
gap> P6 := Group(R.generators);
<matrix group with 1 generators>
gap> Append(names,["ordnung.6/(2)^2(6)^1(18)^1/words.min.292"]);
gap> Append(GROUPS,[P6]);
gap> R := CaratReadBravaisFile("ordnung.6/(2)^2(6)^1(18)^1/min.293");
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 ] ] ], size := 6 )
gap> P7 := Group(R.generators);
<matrix group with 1 generators>
gap> Append(names,["ordnung.6/(2)^2(6)^1(18)^1/words.min.293"]);
gap> Append(GROUPS,[P7]);
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, 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([ [ [ 1, 0, 0, 0, 0, 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, 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, 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, -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([ [ [ -1, 0, 0, 0, 0, 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, 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, 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, -1, 1, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ],
          [ 0, 0, 0, 0, 0, 1 ] ] ]) ]
gap> Print(names,"\n");
[ "ordnung.12/(2)^2(6)^1(18)^1/words.group.1613", 
  "ordnung.12/(2)^3(6)^1/words.group.1614", 
  "ordnung.12/(2)^3(6)^1/words.group.1615", 
  "ordnung.12/(2)^3(6)^1/words.group.1616", 
  "ordnung.24/(2)^3(6)^1/words.group.1617", 
  "ordnung.6/(2)^2(6)^1(18)^1/words.min.292", 
  "ordnung.6/(2)^2(6)^1(18)^1/words.min.293" ]
gap> Size(GROUPS);
7
gap> Size(names);
7
gap> Read("../../TGROUPS.GAP");
gap> for i in [1..Size(GROUPS)] do
>    SubgroupWords(GROUPS[i], names[i]);
> od;
[ 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, x2^4 ]
[ x1, x2^4 ]
[ x1*x2^3, x2^4 ]
[ x2^3, 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 ]
[ x1^3 ]
[ x1^4 ]
[ x1^3 ]
[ x1^2 ]
gap> LogTo();