The homology of $\mathrm{O}\mathrm{u}\mathrm{t}(F_8)$ and $\mathrm{A}\mathrm{u}\mathrm{t}(F_7)$

We compute the rational homology of $\mathrm{O}\mathrm{u}\mathrm{t}(F_8)$ and $\mathrm{A}\mathrm{u}\mathrm{t}(F_7)$, and several related groups. We also show that the Eisenstein classes in $H_7(\mathrm{A}\mathrm{u}\mathrm{t}(F_5))$ and $H_{11}(\mathrm{A}\mathrm{u}\mathrm{t}(F_7))$ are zero.