gap> G:=SpaceGroup(4,2);;
gap> R:=ResolutionCubicalCrystGroup(G,12);
Resolution of length 12 in characteristic 0 for <matrix group with 
5 generators> . 

gap> R!.dimension(5);
16
gap> R!.dimension(7);
16
gap> List([1..16],k->R!.boundary(5,k)=R!.boundary(7,k));
[ true, true, true, true, true, true, true, true, true, true, true, true, 
  true, true, true, true ]

gap> C:=HomToIntegers(R);
Cochain complex of length 12 in characteristic 0 . 

gap> Cohomology(C,0);
[ 0 ]
gap> Cohomology(C,1);
[  ]
gap> Cohomology(C,2);
[ 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0 ]
gap> Cohomology(C,3);
[  ]
gap> Cohomology(C,4);
[ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0 ]
gap> Cohomology(C,5);
[  ]
gap> Cohomology(C,6);
[ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]
gap> Cohomology(C,7);
[  ]

gap> IntegralRingGenerators(R,1);
[  ]
gap> IntegralRingGenerators(R,2);
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], 
  [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ], 
  [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ], 
  [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ], 
  [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ], 
  [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ]
gap> IntegralRingGenerators(R,3);
[  ]
gap> IntegralRingGenerators(R,4);
[  ]
gap> IntegralRingGenerators(R,5);
[  ]
gap> IntegralRingGenerators(R,6);
[  ]
gap> IntegralRingGenerators(R,7);
[  ]
gap> IntegralRingGenerators(R,8);
[  ]
gap> IntegralRingGenerators(R,9);
[  ]
gap> IntegralRingGenerators(R,10);
[  ]