Let $V$ be $n$-dimensional complex vector space with basis $\{e_1,...,e_n\}$ and let $\phi\colon S_n \to GL(V)$ be homomorphism of groups such that $\phi(\sigma)e_j = e_\sigma(j), j = 1,...,n$.
Prove that $G = \operatorname{Im} \phi$ is reflection group and find her exponents.
($S_n$ is symmetric group of order $n$ and $\sigma$ is pseudoreflection).
Hint: $S_n$ is generated by permutations that interchange two numbers while leaving the other $n-2$ numbers fixed. Show that permutations of this sort are sent by $\phi$ to reflections.