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 $g\geq5$.)


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