In a survey paper of [Korkmaz](http://journals.tubitak.gov.tr/math/issues/mat-02-26-1/mat-26-1-8-0203-13.pdf) it is stated that $H\_2(\mathrm{Mod}\_3)$ is either $\Bbb Z$ or $\Bbb Z \oplus \Bbb Z\_2$, but I was not able to find out a precise computation of this group (resolving the ambiguity). Is this group known? Any reference?



Second homology of mapping class group of genus 3
In his paper "Lagrangian mapping class groups from a group homological point of view" (available [here](http://arxiv.org/abs/0910.5262)), Sakasai proves that the desired homology group is $\mathbb{Z} \oplus \mathbb{Z}/2$.


