How can I find all homomorphisms $f:S_n \rightarrow \mathbb Z_n$ for $n > 4$, where $S_n$ is permutation group on $n$ elements and $\mathbb Z_n$ is group mod $n$?
My guess would be that normal subgroups of $S_n$ for $n>4$ are only $1,A_n,S_n$ and then use property of group homomorphisms that $\ker(f)$ is a normal subgroup.