Number of group homomorphism from {$1, \omega, \omega^2$} to $S_{3}$.

Question

Let $G$ denote the group {$1, \omega, \omega^2$} under multiplication where $\omega$ is a complex cube root of unity. How many group homomorphism are there from $G$ to $S_{3}$, the permutation group over $3$ elements? From the concept number of normal subgroup given the possible homomorphism, I find only trivial homomorphism. Is this answer correct?