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Yeah, notation can be a bit of a pain here.
I have given your remark a remark-environment here, instead of it being a subsection, and edited slightly, mostly for formatting.
Great
Is there a citable computation of the group cohomology of dihedral groups with coefficients in $\mathbb{Z}$ equipped with its non-trivial sign action?
This question is also MO:q/141489.
I haven’t checked the two answers there yet, but don’t they contradict each other?
The accepted answer MO:a/141557 sees the cohomology concentrated in odd degrees.
But the other answer MO:a/141546, whose author claims to have checked this with computer algebra, argues for a nontivial contribution in degree 2.
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