gap> G:=SymmetricGroup(6);;

gap> A:=AbelianPcpGroup([0]);;
gap> alpha:=function(g,a); return a^SignPerm(g); end;;
gap> A:=GModuleAsGOuterGroup(G,A,alpha);
ZG-module with abelian invariants [ 0 ] and G= SymmetricGroup( [ 1 .. 6 ] )

gap> R:=ResolutionFiniteGroup(G,5);;
gap> C:=HomToGModule(R,A);
G-cocomplex of length 5 . 

gap> Cohomology(C,4);
[ 2, 2, 5 ]
