A faithful representation of a finite group ${G}$ is one where different elements of ${G}$ induce different linear transformations, i.e. ${G \rightarrow Aut(V)}$ is injective. The result is
Lemma 1 If ${V}$ is a faithful representation of ${G}$, then every simple representation of ${G}$ occurs as a direct summand in some tensor power ${V^{\otimes p}}$  (more…)