gap> RequirePackage("carat");
true
gap> names := [];
[  ]
gap> GROUPS := [];
[  ]
gap> R := CaratReadBravaisFile("ordnung.12/(1)^4(24)^4/min.306");
rec( 
  generators := [ [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, -1, 
              1, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, -1 ], 
          [ 0, 0, 0, 0, -1, 0 ] ], 
      [ [ 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, -1 ], [ 0, 0, 0, 0, 1, 0 ] 
         ] ], size := 12 )
gap> P1 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.12/(1)^4(24)^4/words.min.306"]);
gap> Append(GROUPS,[P1]);
gap> R := CaratReadBravaisFile("ordnung.12/(1)^4(24)^4/min.307");
rec( 
  generators := [ [ [ 0, -1, 0, 0, 0, 0 ], [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 
              -1, 0, 0 ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 0, 1 ], 
          [ 0, 0, 0, 0, 1, 0 ] ], 
      [ [ 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, 1 ], [ 0, 0, 0, 0, -1, 0 ] 
         ] ], size := 12 )
gap> P2 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.12/(1)^4(24)^4/words.min.307"]);
gap> Append(GROUPS,[P2]);
gap> R := CaratReadBravaisFile("ordnung.144/(1)^4(6)^4/group.1667");
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, 0, 1 ], [ 0, 0, 0, 0, 1, 0 ] ], 
      [ [ 0, 0, -1, -1, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], 
          [ -1, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -1, 1 ], [ 0, 0, 0, 0, -1, 0 ] 
         ] ], size := 144 )
gap> P3 := Group(R.generators);
<matrix group with 4 generators>
gap> Append(names,["ordnung.144/(1)^4(6)^4/words.group.1667"]);
gap> Append(GROUPS,[P3]);
gap> R := CaratReadBravaisFile("ordnung.18/(1)^2(6)^3(18)^1/min.308");
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 ], [ 1, 1, 0, 0, 0, 0 ], [ 1, 1, -1, 1, 0, 0 ], 
          [ 1, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, -1, 1 ], [ 0, 0, 0, 0, -1, 0 ] 
         ] ], size := 18 )
gap> P4 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.18/(1)^2(6)^3(18)^1/words.min.308"]);
gap> Append(GROUPS,[P4]);
gap> R := CaratReadBravaisFile("ordnung.18/(1)^2(6)^3(18)^1/min.309");
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 ], [ -1, -1, 0, 0, 0, 0 ], [ -1, -1, 1, -1, 0, 0 ],
          [ -1, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, -1 ], [ 0, 0, 0, 0, 1, 0 ] 
         ] ], size := 18 )
gap> P5 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.18/(1)^2(6)^3(18)^1/words.min.309"]);
gap> Append(GROUPS,[P5]);
gap> R := CaratReadBravaisFile("ordnung.18/(3)^4(6)^4/min.310");
rec( 
  generators := [ [ [ -1, 0, 0, 0, 0, 0 ], [ -1, 1, 0, 0, 0, 0 ], [ 1, 0, 1, 
              0, 0, 0 ], [ -1, 1, -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 ] ]
        , 
      [ [ 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 := 18 )
gap> P6 := Group(R.generators);
<matrix group with 3 generators>
gap> Append(names,["ordnung.18/(3)^4(6)^4/words.min.310"]);
gap> Append(GROUPS,[P6]);
gap> R := CaratReadBravaisFile("ordnung.24/(1)^4(24)^4/group.1668");
rec( 
  generators := [ [ [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 1, 0, 0, 0, 
              0, 0 ], [ 0, 1, 0, 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, 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 := 24 )
gap> P7 := Group(R.generators);
<matrix group with 3 generators>
gap> Append(names,["ordnung.24/(1)^4(24)^4/words.group.1668"]);
gap> Append(GROUPS,[P7]);
gap> R := CaratReadBravaisFile("ordnung.36/(1)^2(2)^1(6)^3/group.1669");
rec( 
  generators := [ [ [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 1, -1, 0, 0 ], [ -1, 1, 0, 
              0, 0, 0 ], [ -1, 0, 0, 0, 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(2)^1(6)^3/words.group.1669"]);
gap> Append(GROUPS,[P8]);
gap> R := CaratReadBravaisFile("ordnung.36/(1)^2(2)^1(6)^3/group.1670");
rec( 
  generators := [ [ [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 1, -1, 0, 0 ], [ -1, 1, 0, 
              0, 0, 0 ], [ -1, 0, 0, 0, 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 := 36 )
gap> P9 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.36/(1)^2(2)^1(6)^3/words.group.1670"]);
gap> Append(GROUPS,[P9]);
gap> R := CaratReadBravaisFile("ordnung.36/(1)^2(2)^1(6)^3/group.1671");
rec( 
  generators := [ [ [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 1, -1, 0, 0 ], [ -1, 1, 0, 
              0, 0, 0 ], [ -1, 0, 0, 0, 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> P10 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.36/(1)^2(2)^1(6)^3/words.group.1671"]);
gap> Append(GROUPS,[P10]);
gap> R := CaratReadBravaisFile("ordnung.36/(1)^2(3)^2(6)^4/group.1672");
rec( 
  generators := [ [ [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 1, -1, 0, 0 ], [ -1, 1, 0, 
              0, 0, 0 ], [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], 
          [ 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, -1 ], [ 0, 0, 0, 0, 0, -1 ] 
         ] ], size := 36 )
gap> P11 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.36/(1)^2(3)^2(6)^4/words.group.1672"]);
gap> Append(GROUPS,[P11]);
gap> R := CaratReadBravaisFile("ordnung.36/(1)^2(3)^2(6)^4/group.1673");
rec( 
  generators := [ [ [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 1, -1, 0, 0 ], [ -1, 1, 0, 
              0, 0, 0 ], [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], 
          [ 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, 1 ], [ 0, 0, 0, 0, 0, 1 ] 
         ] ], size := 36 )
gap> P12 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.36/(1)^2(3)^2(6)^4/words.group.1673"]);
gap> Append(GROUPS,[P12]);
gap> R := CaratReadBravaisFile("ordnung.36/(1)^2(3)^2(6)^4/group.1674");
rec( 
  generators := [ [ [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 1, -1, 0, 0 ], [ -1, 1, 0, 
              0, 0, 0 ], [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], 
          [ 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, 0, 1 ], [ 0, 0, 0, 0, 1, 0 ] ] ]
    , size := 36 )
gap> P13 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.36/(1)^2(3)^2(6)^4/words.group.1674"]);
gap> Append(GROUPS,[P13]);
gap> R := CaratReadBravaisFile("ordnung.36/(1)^2(3)^2(6)^4/group.1675");
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, 1, -1 ] ], 
      [ [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 1, -1, 0, 0 ], [ -1, 1, 0, 0, 0, 0 ], 
          [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -1 ], [ 0, 0, 0, 0, 0, -1 ] 
         ] ], size := 36 )
gap> P14 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.36/(1)^2(3)^2(6)^4/words.group.1675"]);
gap> Append(GROUPS,[P14]);
gap> R := CaratReadBravaisFile("ordnung.36/(1)^2(6)^3(18)^1/group.1676");
rec( 
  generators := [ [ [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 1, -1, 0, 0 ], [ -1, 1, 0, 
              0, 0, 0 ], [ -1, 0, 0, 0, 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> P15 := Group(R.generators);
<matrix group with 2 generators>
gap> Append(names,["ordnung.36/(1)^2(6)^3(18)^1/words.group.1676"]);
gap> Append(GROUPS,[P15]);
gap> R := CaratReadBravaisFile("ordnung.36/(1)^4(6)^4/group.1677");
rec( 
  generators := [ [ [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 1, -1, 0, 0 ], [ -1, 1, 0, 
              0, 0, 0 ], [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], 
          [ 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 ] ],
      [ [ -1, 0, 0, 0, 0, 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> P16 := Group(R.generators);
<matrix group with 3 generators>
gap> Append(names,["ordnung.36/(1)^4(6)^4/words.group.1677"]);
gap> Append(GROUPS,[P16]);
gap> R := CaratReadBravaisFile("ordnung.36/(1)^4(6)^4/group.1678");
rec( 
  generators := [ [ [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 1, -1, 0, 0 ], [ -1, 1, 0, 
              0, 0, 0 ], [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1 ], 
          [ 0, 0, 0, 0, 1, 0 ] ], 
      [ [ 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 := 36 )
gap> P17 := Group(R.generators);
<matrix group with 3 generators>
gap> Append(names,["ordnung.36/(1)^4(6)^4/words.group.1678"]);
gap> Append(GROUPS,[P17]);
gap> R := CaratReadBravaisFile("ordnung.36/(3)^4(6)^4/group.1679");
rec( 
  generators := [ [ [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 1, -1, 0, 0 ], [ -1, 1, 0, 
              0, 0, 0 ], [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], 
          [ 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 ] ],
      [ [ -1, 0, 0, 0, 0, 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> P18 := Group(R.generators);
<matrix group with 3 generators>
gap> Append(names,["ordnung.36/(3)^4(6)^4/words.group.1679"]);
gap> Append(GROUPS,[P18]);
gap> R := CaratReadBravaisFile("ordnung.72/(1)^2(2)^1(6)^3/group.1680");
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, 0, -1, -1, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], 
          [ -1, 1, 0, 0, 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 := 72 )
gap> P19 := Group(R.generators);
<matrix group with 3 generators>
gap> Append(names,["ordnung.72/(1)^2(2)^1(6)^3/words.group.1680"]);
gap> Append(GROUPS,[P19]);
gap> R := CaratReadBravaisFile("ordnung.72/(1)^2(3)^2(6)^4/group.1681");
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, 0, -1, -1, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], 
          [ -1, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -1, 1 ], [ 0, 0, 0, 0, -1, 0 ] 
         ], 
      [ [ -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, 0, -1 ], 
          [ 0, 0, 0, 0, -1, 0 ] ] ], size := 72 )
gap> P20 := Group(R.generators);
<matrix group with 3 generators>
gap> Append(names,["ordnung.72/(1)^2(3)^2(6)^4/words.group.1681"]);
gap> Append(GROUPS,[P20]);
gap> R := CaratReadBravaisFile("ordnung.72/(1)^4(6)^4/group.1682");
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, 0 ] ], 
      [ [ 0, 0, -1, -1, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], 
          [ -1, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -1, 1 ], [ 0, 0, 0, 0, -1, 0 ] 
         ] ], size := 72 )
gap> P21 := Group(R.generators);
<matrix group with 3 generators>
gap> Append(names,["ordnung.72/(1)^4(6)^4/words.group.1682"]);
gap> Append(GROUPS,[P21]);
gap> R := CaratReadBravaisFile("ordnung.72/(1)^4(6)^4/group.1683");
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, 0, -1, -1, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], 
          [ -1, 1, 0, 0, 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, -1, -1, 0, 0 ], 
          [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0 ] ] ]
    , size := 72 )
gap> P22 := Group(R.generators);
<matrix group with 3 generators>
gap> Append(names,["ordnung.72/(1)^4(6)^4/words.group.1683"]);
gap> Append(GROUPS,[P22]);
gap> R := CaratReadBravaisFile("ordnung.72/(1)^4(6)^4/group.1684");
rec( 
  generators := [ [ [ 0, 0, -1, -1, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, -1, 
              0, 0, 0, 0 ], [ -1, 1, 0, 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 ] 
         ], 
      [ [ 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 := 72 )
gap> P23 := Group(R.generators);
<matrix group with 3 generators>
gap> Append(names,["ordnung.72/(1)^4(6)^4/words.group.1684"]);
gap> Append(GROUPS,[P23]);
gap> R := CaratReadBravaisFile("ordnung.72/(1)^4(6)^4/group.1685");
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, 0, 1 ], [ 0, 0, 0, 0, 1, 0 ] ]
        , 
      [ [ 0, 0, -1, -1, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], 
          [ -1, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -1, 1 ], [ 0, 0, 0, 0, -1, 0 ] 
         ] ], size := 72 )
gap> P24 := Group(R.generators);
<matrix group with 3 generators>
gap> Append(names,["ordnung.72/(1)^4(6)^4/words.group.1685"]);
gap> Append(GROUPS,[P24]);
gap> R := CaratReadBravaisFile("ordnung.72/(1)^4(6)^4/group.1686");
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, 0, 1, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], 
          [ 1, -1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -1, 1 ], [ 0, 0, 0, 0, -1, 0 ] 
         ], 
      [ [ 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, 0, 1 ], [ 0, 0, 0, 0, 1, 0 ] ] ]
    , size := 72 )
gap> P25 := Group(R.generators);
<matrix group with 3 generators>
gap> Append(names,["ordnung.72/(1)^4(6)^4/words.group.1686"]);
gap> Append(GROUPS,[P25]);
gap> Print(GROUPS,"\n");
[ Group(
    [ [ [ 0, 1, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], [ 0, 0, -1, 1, 0, 0 ], 
          [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, -1 ], [ 0, 0, 0, 0, -1, 0 ] ]
        , 
      [ [ 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, -1 ], [ 0, 0, 0, 0, 1, 0 ] 
         ] ]), 
  Group([ [ [ 0, -1, 0, 0, 0, 0 ], [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, -1, 0, 0 
             ], [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 0, 1 ], 
          [ 0, 0, 0, 0, 1, 0 ] ], 
      [ [ 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, 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, 0, 0, 0, 0, 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, 0 ] ], 
      [ [ 0, 0, -1, -1, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], 
          [ -1, 1, 0, 0, 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 ], [ 1, 1, 0, 0, 0, 0 ], [ 1, 1, -1, 1, 0, 0 ], 
          [ 1, 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 ], [ -1, -1, 0, 0, 0, 0 ], [ -1, -1, 1, -1, 0, 0 ],
          [ -1, 0, 0, -1, 0, 0 ], [ 0, 0, 0, 0, 1, -1 ], [ 0, 0, 0, 0, 1, 0 ] 
         ] ]), 
  Group([ [ [ -1, 0, 0, 0, 0, 0 ], [ -1, 1, 0, 0, 0, 0 ], [ 1, 0, 1, 0, 0, 0 ]
            , [ -1, 1, -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 ] ]
        , 
      [ [ 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, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 1, 0, 0, 0, 0, 0 ], 
          [ 0, 1, 0, 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, 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([ [ [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 1, -1, 0, 0 ], [ -1, 1, 0, 0, 0, 0 
             ], [ -1, 0, 0, 0, 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, 0, 0, -1, 0, 0 ], [ 0, 0, 1, -1, 0, 0 ], [ -1, 1, 0, 0, 0, 0 
             ], [ -1, 0, 0, 0, 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([ [ [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 1, -1, 0, 0 ], [ -1, 1, 0, 0, 0, 0 
             ], [ -1, 0, 0, 0, 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, 0, 0, -1, 0, 0 ], [ 0, 0, 1, -1, 0, 0 ], [ -1, 1, 0, 0, 0, 0 
             ], [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], 
          [ 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, -1 ], [ 0, 0, 0, 0, 0, -1 ] 
         ] ]), 
  Group([ [ [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 1, -1, 0, 0 ], [ -1, 1, 0, 0, 0, 0 
             ], [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], 
          [ 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, 1 ], [ 0, 0, 0, 0, 0, 1 ] 
         ] ]), 
  Group([ [ [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 1, -1, 0, 0 ], [ -1, 1, 0, 0, 0, 0 
             ], [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], 
          [ 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, 0, 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, 1, -1 ] ], 
      [ [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 1, -1, 0, 0 ], [ -1, 1, 0, 0, 0, 0 ], 
          [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, -1 ], [ 0, 0, 0, 0, 0, -1 ] 
         ] ]), 
  Group([ [ [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 1, -1, 0, 0 ], [ -1, 1, 0, 0, 0, 0 
             ], [ -1, 0, 0, 0, 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, 0, 0, -1, 0, 0 ], [ 0, 0, 1, -1, 0, 0 ], [ -1, 1, 0, 0, 0, 0 
             ], [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], 
          [ 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 ] ],
      [ [ -1, 0, 0, 0, 0, 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, 0, 0, -1, 0, 0 ], [ 0, 0, 1, -1, 0, 0 ], [ -1, 1, 0, 0, 0, 0 
             ], [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1 ], 
          [ 0, 0, 0, 0, 1, 0 ] ], 
      [ [ 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 ] ] 
     ]), 
  Group([ [ [ 0, 0, 0, -1, 0, 0 ], [ 0, 0, 1, -1, 0, 0 ], [ -1, 1, 0, 0, 0, 0 
             ], [ -1, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -1, 0 ], 
          [ 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 ] ],
      [ [ -1, 0, 0, 0, 0, 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, -1, 0 ], [ 0, 0, 0, 0, 0, -1 ] ]
        , 
      [ [ 0, 0, -1, -1, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], 
          [ -1, 1, 0, 0, 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([ [ [ -1, 0, 0, 0, 0, 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, 0, -1, -1, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], 
          [ -1, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -1, 1 ], [ 0, 0, 0, 0, -1, 0 ] 
         ], 
      [ [ -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, 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, 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, 0 ] ], 
      [ [ 0, 0, -1, -1, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], 
          [ -1, 1, 0, 0, 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 ] ], 
      [ [ 0, 0, -1, -1, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], 
          [ -1, 1, 0, 0, 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, -1, -1, 0, 0 ], 
          [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, 0, 1, 0 ] ] 
     ]), 
  Group([ [ [ 0, 0, -1, -1, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 
              0 ], [ -1, 1, 0, 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 ] 
         ], 
      [ [ 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, 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, 0, 1 ], [ 0, 0, 0, 0, 1, 0 ] ]
        , 
      [ [ 0, 0, -1, -1, 0, 0 ], [ 0, 0, -1, 0, 0, 0 ], [ 0, -1, 0, 0, 0, 0 ], 
          [ -1, 1, 0, 0, 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 ] ]
        , [ [ 0, 0, 1, 1, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], 
          [ 1, -1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, -1, 1 ], [ 0, 0, 0, 0, -1, 0 ] 
         ], 
      [ [ 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, 0, 1 ], [ 0, 0, 0, 0, 1, 0 ] ] 
     ]) ]
gap> Print(names,"\n");
[ "ordnung.12/(1)^4(24)^4/words.min.306", 
  "ordnung.12/(1)^4(24)^4/words.min.307", 
  "ordnung.144/(1)^4(6)^4/words.group.1667", 
  "ordnung.18/(1)^2(6)^3(18)^1/words.min.308", 
  "ordnung.18/(1)^2(6)^3(18)^1/words.min.309", 
  "ordnung.18/(3)^4(6)^4/words.min.310", 
  "ordnung.24/(1)^4(24)^4/words.group.1668", 
  "ordnung.36/(1)^2(2)^1(6)^3/words.group.1669", 
  "ordnung.36/(1)^2(2)^1(6)^3/words.group.1670", 
  "ordnung.36/(1)^2(2)^1(6)^3/words.group.1671", 
  "ordnung.36/(1)^2(3)^2(6)^4/words.group.1672", 
  "ordnung.36/(1)^2(3)^2(6)^4/words.group.1673", 
  "ordnung.36/(1)^2(3)^2(6)^4/words.group.1674", 
  "ordnung.36/(1)^2(3)^2(6)^4/words.group.1675", 
  "ordnung.36/(1)^2(6)^3(18)^1/words.group.1676", 
  "ordnung.36/(1)^4(6)^4/words.group.1677", 
  "ordnung.36/(1)^4(6)^4/words.group.1678", 
  "ordnung.36/(3)^4(6)^4/words.group.1679", 
  "ordnung.72/(1)^2(2)^1(6)^3/words.group.1680", 
  "ordnung.72/(1)^2(3)^2(6)^4/words.group.1681", 
  "ordnung.72/(1)^4(6)^4/words.group.1682", 
  "ordnung.72/(1)^4(6)^4/words.group.1683", 
  "ordnung.72/(1)^4(6)^4/words.group.1684", 
  "ordnung.72/(1)^4(6)^4/words.group.1685", 
  "ordnung.72/(1)^4(6)^4/words.group.1686" ]
gap> Size(GROUPS);
25
gap> Size(names);
25
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 ]
[ x4^3, x2, x1, x3^2, x4^2 ]
[ x4^3, x2, x2*x3^2*x4^2*x3, x3^2, x4^2 ]
[ x4^3, x2, x1*x2*x3^2*x4^2*x3, x3^2, x4^2 ]
[ x4^3, x1, x2*x3^2*x4^2*x3, x3^2, x4^2 ]
[ x4^3, x3^2*x4^2*x3, x1, x3^2, x4^2 ]
[ x4^3, x1*x2, x2*x3^2*x4^2*x3, x3^2, x4^2 ]
[ x4^3, x3^2*x4^2*x3, x1*x2*x3^2*x4^2*x3, x3^2, x4^2 ]
[ x2, x1, x2*x3^2*x4^2*x3, x3^2, x4^2 ]
[ x2*x3^3*x4, x2, x1, x3^2, x4^2 ]
[ x1*x4^3, x2, x2*x3^2*x4^2*x3, x3^2, x4^2 ]
[ x2*x3^3*x4, x2, x1*x2*x3^2*x4^2*x3, x3^2, x4^2 ]
[ x2*x4^3, x1, x2*x3^2*x4^2*x3, x3^2, x4^2 ]
[ x2*x3^3*x4, x3^2*x4^2*x3, x1, x3^2, x4^2 ]
[ x1*x4^3, x1*x2, x2*x3^2*x4^2*x3, x3^2, x4^2 ]
[ x2*x3^3*x4, x3^2*x4^2*x3, x1*x2*x3^2*x4^2*x3, x3^2, x4^2 ]
[ x4^3, x2, x1, x2*x3^2*x4^2*x3, x4^2 ]
[ x4^3, x2, x1, x2*x3^2*x4^2*x3, x3^2 ]
[ x2^2, x1^2 ]
[ x2^3, x1^2 ]
[ x2^3, x2^2 ]
[ x2^2, x1^2 ]
[ x1^2*x2^3, x1^2 ]
[ x1^2*x2^3, x2^2 ]
[ x2*x1*x3*x1, x1*x2*x1 ]
[ x1, x2*x1*x3*x1 ]
[ x1, x1*x2*x1 ]
[ x1, x1*x2*x3*x1 ]
[ x1, x1*x3*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 ]
[ x2^3, x1^2, x2^2 ]
[ x1^3, x1^2, x2^2 ]
[ x1^3*x2^3, x1^2, x2^2 ]
[ x2^3, x1^3, x2^2 ]
[ x2^3, x1^3, x1^2 ]
[ x2^3, x1*x2*x1*x2, x1*x2^2*x1*x2^4 ]
[ x1, x1*x2*x1*x2, x1*x2^2*x1*x2^4 ]
[ x1*x2^3, x1*x2*x1*x2, x1*x2^2*x1*x2^4 ]
[ x2^3, x1, x1*x2^2*x1*x2^4 ]
[ x2^3, x1, x1*x2*x1*x2 ]
[ x2^3, x1^2, x2^2 ]
[ x1^3, x1^2, x2^2 ]
[ x1^3*x2^3, x1^2, x2^2 ]
[ x2^3, x1^3, x2^2 ]
[ x2^3, x1^3, x1^2 ]
[ x2*x1*x2*x1*x2^3, x1*x2*x1*x2, x1*x2*x1*x2^3 ]
[ x1, x1*x2*x1*x2, x1*x2*x1*x2^3 ]
[ x1*x2*x1*x2*x1*x2^3, x1*x2*x1*x2, x1*x2*x1*x2^3 ]
[ x2*x1*x2*x1*x2^3, x1, x1*x2*x1*x2 ]
[ x2*x1*x2*x1*x2^3, x1, x1*x2^2*x1 ]
[ x1*x2^3*x1, x1*x2*x1*x2, x1*x2*x1*x2^3 ]
[ x2*x1*x2, x1*x2*x1*x2, x1*x2*x1*x2^3 ]
[ x1*x2*x1*x2*x1*x2^3, x1*x2*x1*x2, x1*x2*x1*x2^3 ]
[ x1*x2^3*x1, x2*x1*x2, x1*x2*x1*x2 ]
[ x1*x2^3*x1, x2*x1*x2, x1*x2^2*x1 ]
[ x2*x1*x2*x1*x2^3, x1*x2*x1*x2, x1*x2*x1*x2^3 ]
[ x1, x1*x2*x1*x2, x1*x2*x1*x2^3 ]
[ x1*x2*x1*x2*x1*x2^3, x1*x2*x1*x2, x1*x2*x1*x2^3 ]
[ x2*x1*x2*x1*x2^3, x1, x1*x2^2*x1 ]
[ x2*x1*x2*x1*x2^3, x1, x1*x2*x1*x2 ]
[ x2*x1*x2*x1*x2, x1^2, x1*x2*x1*x2 ]
[ x1^3, x1^2, x1*x2*x1*x2 ]
[ x1^3*x2*x1*x2*x1*x2, x1^2, x1*x2*x1*x2 ]
[ x2*x1*x2*x1*x2, x1^3, x1*x2*x1*x2 ]
[ x2*x1*x2*x1*x2, x1^3, x1^2 ]
[ x2^3, x1^2, x2^2 ]
[ x1^3, x1^2, x2^2 ]
[ x1^3*x2^3, x1^2, x2^2 ]
[ x2^3, x1^3, x2^2 ]
[ x2^3, x1^3, x1^2 ]
[ x3^3, x1*x2*x1, x3^2 ]
[ x1*x3^2, x1*x2*x1, x3^2 ]
[ x3*x1, x1*x2*x1, x3^2 ]
[ x3^3, x1*x3^2, x1*x2*x1 ]
[ x3^3, x1*x3^2, x3^2 ]
[ x3^3, x1*x3^2, x1*x2*x3^2*x1 ]
[ x3^3, x1*x3^2, x1*x2*x1*x3^2 ]
[ x1*x3^3, x1*x2*x1, x3^2 ]
[ x1, x1*x2*x1, x3^2 ]
[ x3^3, x1*x2*x1, x3^2 ]
[ x1*x3^3, x1, x1*x2*x1 ]
[ x1*x3^3, x1, x3^2 ]
[ x1*x3^3, x1, x1*x2*x3^2*x1 ]
[ x1*x3^3, x1, x1*x2*x1*x3^2 ]
[ x1*x3^3, x1*x2*x1, x3^2 ]
[ x1, x1*x2*x1, x3^2 ]
[ x3^3, x1*x2*x1, x3^2 ]
[ x1*x3^3, x1, x1*x2*x1 ]
[ x1*x3^3, x1, x3^2 ]
[ x1*x3^3, x1, x1*x2*x3^2*x1 ]
[ x1*x3^3, x1, x1*x2*x1*x3^2 ]
[ x3^3, x2^3, x2^4, x3^2 ]
[ x3^3, x1, x2^4, x3^2 ]
[ x3^3, x1*x2^3, x2^4, x3^2 ]
[ x2^3, x1, x2^4, x3^2 ]
[ x1*x3^3, x2^3, x2^4, x3^2 ]
[ x2^3*x3^3, x1, x2^4, x3^2 ]
[ x1*x3^3, x1*x2^3, x2^4, x3^2 ]
[ x3^3, x2^3, x1, x3^2 ]
[ x3^3, x2^3, x1, x2^4 ]
[ x2^2*x3^3, x1, x2^4, x3^2 ]
[ x2^2*x3^3, x2^3, x2^4, x3^2 ]
[ x2^2*x3^3, x1*x2^3, x2^4, x3^2 ]
[ x1, x2^3, x2^4, x3^2 ]
[ x2^5*x3^3, x1, x2^4, x3^2 ]
[ x1*x2^2*x3^3, x2^3, x2^4, x3^2 ]
[ x2^5*x3^3, x1*x2^3, x2^4, x3^2 ]
[ x2^2*x3^3, x1, x2^3, x3^2 ]
[ x2^2*x3^3, x1, x2^3, x2^4 ]
[ x3^3, x1, x2^2, x3^2 ]
[ x3^3, x2^3, x2^2, x3^2 ]
[ x3^3, x1*x2^3, x2^2, x3^2 ]
[ x1, x2^3, x2^2, x3^2 ]
[ x2^3*x3^3, x1, x2^2, x3^2 ]
[ x1*x3^3, x2^3, x2^2, x3^2 ]
[ x2^3*x3^3, x1*x2^3, x2^2, x3^2 ]
[ x3^3, x1, x2^3, x2^2 ]
[ x3^3, x1, x2^3, x3^2 ]
[ x2^5*x3^3, x1, x2^4, x3^2 ]
[ x2^5*x3^3, x2^3, x2^4, x3^2 ]
[ x2^5*x3^3, x1*x2^3, x2^4, x3^2 ]
[ x1, x2^3, x2^4, x3^2 ]
[ x2^2*x3^3, x1, x2^4, x3^2 ]
[ x1*x2^5*x3^3, x2^3, x2^4, x3^2 ]
[ x2^2*x3^3, x1*x2^3, x2^4, x3^2 ]
[ x2^5*x3^3, x1, x2^3, x2^4 ]
[ x2^5*x3^3, x1, x2^3, x3^2 ]
[ x1*x3^3, x2^3, x3^2, x2^2 ]
[ x1*x3^3, x1, x3^2, x2^2 ]
[ x1*x3^3, x1*x2^3, x3^2, x2^2 ]
[ x2^3, x1, x3^2, x2^2 ]
[ x3^3, x2^3, x3^2, x2^2 ]
[ x1*x2^3*x3^3, x1, x3^2, x2^2 ]
[ x3^3, x1*x2^3, x3^2, x2^2 ]
[ x1*x3^3, x2^3, x1, x3^2 ]
[ x1*x3^3, x2^3, x1, x2^2 ]
[ x1*x3^3, x2^3, x1, x1*x2^2*x1*x3^2 ]
[ x1*x3^3, x2^3, x1, x2^2*x3^2 ]
[ x3^3, x1, x2^2, x3^2 ]
[ x3^3, x1*x2^2*x3^2*x2, x2^2, x3^2 ]
[ x3^3, x2^2*x3^2*x2, x2^2, x3^2 ]
[ x1, x1*x2^2*x3^2*x2, x2^2, x3^2 ]
[ x1*x2^3*x3, x1, x2^2, x3^2 ]
[ x1*x3^3, x1*x2^2*x3^2*x2, x2^2, x3^2 ]
[ x1*x2^3*x3, x2^2*x3^2*x2, x2^2, x3^2 ]
[ x3^3, x1, x1*x2^2*x3^2*x2, x3^2 ]
[ x3^3, x1, x1*x2^2*x3^2*x2, x2^2 ]
[ x3^3, x1, x2^2, x3^2 ]
[ x3^3, x2^3, x2^2, x3^2 ]
[ x3^3, x1*x2^3, x2^2, x3^2 ]
[ x1, x2^3, x2^2, x3^2 ]
[ x2^3*x3^3, x1, x2^2, x3^2 ]
[ x1*x3^3, x2^3, x2^2, x3^2 ]
[ x2^3*x3^3, x1*x2^3, x2^2, x3^2 ]
[ x3^3, x1, x2^3, x3^2 ]
[ x3^3, x1, x2^3, x2^2 ]
gap> LogTo();