TITLE: Calculations of nonabelian group cohomology of R^n
QUESTION [9 upvotes]: I am looking at $H^1(\mathbb{R}^n,G)$ where $G$ is a finite 2-group. I'm wondering if such things have been calculated. I'm afraid I can't say I know anything here, past the result that this calculates group extensions of $\mathbb{R}^n$ by $G$.
Any related literature would also be appreciated.

REPLY [10 votes]: I assume that you are looking at group cohomology. Then the action of $\Bbb{R}^n$ on $G$ is necessarily trivial, so $H^1(\Bbb{R}^n,G)$ is just $\mathrm{Hom}(\Bbb{R}^n,G)$ mod. conjugacy by $G$. But this is of course trivial - $\Bbb{R}^n$ has no finite quotient.