for a finite group G and a trivial abelian G module A, there is the short exact sequence
$0 \rightarrow Ext^1 (G_{ab},A) \rightarrow H^2(G,A) \rightarrow Hom (H_2 (G,Z), A) \rightarrow 0$
I'm looking for a description for the connecting maps. Specially, I want to use the representation of $H_2(G,Z)$ as $M(G)=[F,F]\cap R/ [F,R]$ where $G\cong F/R$ and F is free.