GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
gap> START_TEST("HAP library"); gap> GroupHomology(AlternatingGroup(5),2,2); [ 2 ] gap> GroupHomology(SmallGroup(32,3),4,2); [ 2, 2, 2, 2, 2 ] gap> GroupHomology(AbelianGroup([2,4,6]),4); [ 2, 2, 2, 2, 2, 2, 2, 2 ] gap> GroupHomology([[1,[2,3]],[2,[3,4]]],2); [ 0, 0 ] gap> R:=ResolutionNilpotentGroup(SmallGroup(64,135),5);; gap> TR:=TensorWithIntegers(R);; gap> H4:=Homology(TR,4); [ 2, 2, 2, 2, 2, 2, 2 ] gap> H4a:=IntegralRingGenerators(R,4); [ [ 0, 0, 1, 1, 0, -4, -4 ], [ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ] gap> Tensor:=ThirdHomotopyGroupOfSuspensionB(SymmetricGroup(3)); [ 2 ] gap> Tensor2:=ThirdHomotopyGroupOfSuspensionB(SymmetricGroup(3),12); [ 2 ] gap> R:=ResolutionAbelianGroup([0,0,0],5);; gap> H6:=Homology(TensorWithIntegers(R),3); [ 0 ] gap> H7:=Cohomology(HomToIntegersModP(R,2),3); 1 gap> IsSuperperfect(PerfectGroup(120,1)); true gap> CoefficientsOfUnivariateRationalFunction(PoincareSeries(SmallGroup(64,134))); [ [ 1 ], [ 1, -3, 3, -1 ], 0 ] gap> STOP_TEST( "tst.tst", 1000 );