What is $S^3/\Gamma$? Let G is a group and H is a subgroup of G. I know $G/H$ is the quotient space but I have no idea about what $S^3/\Gamma$ is, where $S^3$ is the sphere and $\Gamma$ is a finite subgroup of $SO(4)$. In this case $S^3$ has not structure of a group and $\Gamma$ is not subgroup of the sphere. So, what is $S^3/\Gamma$?
Thanks for your help.

$\mathrm{SO}(4)$ acts on $S^3$ in the obvious way if we think of $S^3$ as the set of unit vectors in $\Bbb R^4$. Then any subgroup $\Gamma \leq G$ acts on $S^3$ as well. $S^3/\Gamma$ is the the orbit space of this $\Gamma$-action, i.e.
$$S^3/\Gamma = S^3/\!\sim$$
where
$$x \sim y \quad \iff \quad x = g \cdot y \text{ for some } g \in \Gamma.$$
