I have two finite groups. The irreducible representations of their product are given by tensor products of the irreducible of representations of the groups.
Is there a way to build the irreducible representations of a semidirect product from the irreducible representations of the groups?
Any references are very welcome. I couldn't find this in Serre, so I'm guessing it isn't straightforward like the product case. So, any tips would also be great.
Just in case it is completely known and available in the literature, I am interested in $SL_2(\mathbb{F_q})\rtimes H$, where $H$ is the Heisenberg group.