I’ve been studying the group of $\mathbb{Z}$-points of the simply connected Chevalley–Demazure group scheme of type $E_7$, denoted $G_{\text{sc}}(E_7,\mathbb{Z})$; see [Vavilov and Plotkin - Chevalley groups over commutative rings: I. Elementary calculations](https://doi.org/10.1007/BF00047884) for reference. In particular, I am interested in its first three integral homology groups. I have been able to compute the first two homology groups using various results in the literature. However, I have not found anything that helps compute the third homology group. Is there a way to compute this using results from the literature? Maybe there is a more general procedure to apply to this case as was applied in Theo Johnson-Freyd's [answer](https://mathoverflow.net/a/258533) to [H_3 of SL(n,Z) and SL(n,F_p)][2]?

If we can’t determine the third homology, then what can we say about it; for example, can we determine if it has 3-torsion, or it’s order?

  [1]: https://link.springer.com/article/10.1007/BF00047884
  [2]: https://mathoverflow.net/questions/258491/h-3-of-sln-z-and-sln-f-p