File: 7.3.txt

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gap> G:=SpaceGroupIT(3,226);
SpaceGroupOnRightIT(3,226,'1')
gap> R:=ResolutionSpaceGroup(G,15);
Resolution of length 15 in characteristic 0 for <matrix group with 
8 generators> . 
No contracting homotopy available. 

gap> D:=List([0..14],n->Cohomology(HomToIntegersModP(R,2),n));
[ 1, 2, 5, 9, 11, 15, 20, 23, 28, 34, 38, 44, 51, 56, 63 ]

gap> PoincareSeries(D,14);
(-2*x_1^4+2*x_1^2+1)/(-x_1^5+2*x_1^4-x_1^3+x_1^2-2*x_1+1)