[GAP Forum] a variant of Schur covers

[Markus Szymik]

Dear GAP Forum

I understand that GAP comes with two ways to construct Schur covers of a finite p--group G: via SchurCover( G ) or using the functions in the package 'cohomolo.' The result in either case is a central extension E of G with kernel isomorphic to H_2( G; ZZ ) or the p--part thereof. I would like to construct the central extension with kernel H_2( G; ZZ/p ) instead. To illustrate the difference: If the group G is of order 2, we have H_2 ( G; ZZ ) = 0, so that both ways produce E = G, whereas H_2 ( G; ZZ/2 ) = ZZ/2, and I would like to get E = ZZ/4 accordingly. Is there a simple way to achieve this in GAP?

Thanks and all the best

Markus