# Second cohomology of handlebody mapping class group

Let $$H$$ be a genus $$g$$ handlebody, let $$\mathrm{Mod}(H)$$ be its mapping class group. Is the calculation of $$H^2(\mathrm{Mod}(H),\mathbb{Z})$$ known?

(Let $$S$$ be the boundary of $$H$$, then $$\mathrm{Mod}(H)$$ is subgroup of $$\mathrm{Mod}(S)$$ via taking boundary. Harer shown that $$\mathrm{H}^2(\mathrm{Mod}(S),\mathbb{Z})=\mathbb{Z}\oplus\frac{\mathbb{Z}}{(2g-2)\mathbb{Z}}$$ for $$g\geq5$$.)