COMPUTING SECOND COHOMOLOGY OF FINITE GROUPS WITH TRIVIAL COEFFICIENTS Graham Ellis and Irina Kholodna 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 {\scshape Magma} implementation of the procedure.