How to show that the restriction of $\pi$ to the subrepresentation $W$ factor through $G/N$?

Question

I am reading the lecture notes. On Page 16, Line 1, it is said that the restriction of $\pi$ to the subrepresentation $W$ factor through $G/N$. What does "factor through" mean? How to show that the restriction of $\pi$ to the subrepresentation $W$ factor through $G/N$? Thank you very much.

Answer 1

"Factors" means that for the morphism $\pi|_W:G\to {\rm End}W$ there is a morphism $\alpha:G/N\to {\rm End}W$ such that $\pi=\alpha f$ where $f:G\to G/N$ is a canonical epimorphism.