Suppose $G$ is a finite group and $\rho$ is a representation such that $\rho : G \rightarrow GL(V)$. Suppose that $G/ker(\rho)$ is Abelian. What does this tell us about $\rho$? In particular, how can we reach the conclusion that $\rho$ is the direct product of one-dimensional representations of $G$? I feel Maschke's theorem would be useful here, but I need some guidance.
This is an assignment question, so I am mainly looking for hints not full solutions. I want to figure it out on my own with hints and I hope to delete the question once I get an idea.