For a finite group $G$ with a representation $\pi:G\to GL_n(\mathbb C)$ one can define the adjoint representation $Ad$ as the non-trivial summand in $End(\pi)$, i.e. $End(\pi)=\pi\otimes \pi^{\vee}=1\oplus Ad(\pi)$.

For example, if $\pi$ is self-dual then $\pi\otimes \pi=Sym^2(\pi)\oplus \bigwedge^2(\pi)$, and for $n>2$ it is possible to show that $Ad(\pi)$ is reducible.

Are there any known examples when $Ad(\pi)$ is irreducible ?