Let $G$ be a finite group, $n(G)$ the minimal number of generators and $m(G)$ the minimal number of irreducible complex representations generating (with $\otimes$ and $\oplus$) the left regular representation.

*Notation*: the word "generating" does not mean "generating exactly", but as a direct factor.

*Question*: Is it true that $n(G) \ge m(G)$ ?

*Remark*: a group $G$ is linearly primitive iff $m(G) = 1$, so it's obviouly true in this case.