gap> G:=AlternatingGroup(5);;
gap> pi:=PermToMatrixGroup(SymmetricGroup(5),5);;
gap> R:=ResolutionFiniteGroup(G,7);;
gap> C:=HomToIntegralModule(R,pi);;
gap> Cohomology(C,6);
[ 2, 6 ]

gap> D:=TensorWithIntegralModule(R,pi);;
gap> Homology(D,6);
[ 2 ]
