Let G = < X | R > be a finitely presented group acting on a KG-module M, with |X| = r, |R| = s, dim(M) = n. In the first talk, we showed how the first cohomology group H1(G,M) could be computed as
In this talk, we discuss the computation of H2(G,M). This is another important object to compute because the group extensions
Once again, the main effort of the computation occurs in the calculation of the nullspace of a certain matrix. This works out nicely when G is a pc-group, but for a general finite group we have to work harder to reduce the size of the matrix involved. If G is a permutation group, then we can sometimes make use of a base and strong generating set to reduce this size to manageable proportions. Furthermore, if we are only interested in the order of the group H2(G,M), rather than in constructing the extensions explicitly, then we can use some cohomology theory to reduce the computation from G to certain p-subgroups of G.