The paper describes a simple procedure for computing the second cohomology $H^2(G,A)$ of a finitely presented finite group $G$ with coefficients in a finitely presented finite abelian group $A$. An accompanying text-file contains a MAGMA implementation of the procedure.
"Computing second cohomology of finite groups with trivial coefficients." Homology Homotopy Appl. 1 (1) 163 - 168, 1999.