The following result was mentionned earlier in [this thread][1], I searched a bit in the related threads and couldn't find a proof. I would really like to see a proof of it:

Let $G$ be a finite group and $\rho : G \rightarrow GL(\mathbb{C}, n)$ a faithful representation of $G$. Then every irreducible representation of $G$ is contained in some tensor power of $\rho$.


  [1]: https://mathoverflow.net/questions/18132/faithful-characters-of-finite-groups