  Given a finitely presented group $G$, Hopf's formula expresses the second
integral homology of $G$ in terms of generators and relators. We give an
algorithm that exploits Hopf's formula to estimate $H_2(G;k)$, with
coefficients in a finite field k, and give examples using $G=SL_2$ over
specific rings of integers. These examples are related to a conjecture of
Quillen.
