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 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 to H_3 of SL(n,Z) and SL(n,F_p)?

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 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 to H_3 of SL(n,Z) and SL(n,F_p)?

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?

I’ve been studying the group of $\mathbb{Z}$-points of the simply connected Chevalley-Demazure group scheme of type $E_7$, denoted $G_{\mathrm{sc}}(E_7,\mathbb{Z})$; see here 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 the answer here?

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 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 to H_3 of SL(n,Z) and SL(n,F_p)?