Find all homomorphism from $S_4$ to $z_m$.
The only normal subgroup of $S_4$ are trivial , entire group, $A_4$ and klein 4 group.
If m is odd , then there is only one homomorphism (trivial)... What if n is even?
My attempt.
If $6|n$ then there is 3 homomorphism of whose kernal is {e},$A_4$, klein 4 group. If $6 $ doesn't divide $n$ then there is only 2 homomorphism... Is this correct?