Homology of group rings

Question

Let $\mathbb Z G$ be the group ring of $G$. Denote by $\mathbb Z G ^{gp}$ the universal enveloping group of the monoid $(\mathbb Z G,*)$, i.e. the fundamental group of the classyfiyng space of $(\mathbb Z G,*)$. How to compute $H_* (\mathbb Z G ^{gp},\mathbb Z )=H_* (B (\mathbb Z G,*),\mathbb Z )$ in terms of $H_* (G,\mathbb Z )$?