Hi!

I'm sure it is well known but i don't know enough algebraic topology... Let $k\geq 2$, $$S^{2k-1}\hookrightarrow \mathbb{C}^{k}$$ be the unit sphere and $G$ be a finite subgroup of $U(k)$ acting linearly (the action is induced by the one on $\mathbb{C}^{k}$) and freely on $S^{2k-1}$ so the quotient $S^{2k-1}/G$ is a manifold. Is there a quick and dirty method to calculate $H^{2}(S^{2k-1}/G,\mathbb{Z})$? I could be happy with $H^{2}(S^{2k-1}/G,\mathbb{R})$ but it would be better $H^{2}(S^{2k-1}/G,\mathbb{Z})$.

Thank you in advance!