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Hi, I am wondering if anything is known about irreducible representations of a semidirect product over $C_p:=\mathbb{Z} / p \mathbb{Z}$ in general or at least in special cases. For example of $C_q \rtimes C_l$ over $C_p$, where $p,q,l$ are some primes. Is there any well-known literature?

Thank you for hints!

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Look at Weintraub "Representation theory ... " for Mackey Machine (pg 120 or so).

Edit in response to Mackey Maschine for semidirect product. The reference does not give a solution to the problem, but studying the Mackey machine/Clifford theory seems like the right starting point for a semidirect product.

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    $\begingroup$ For finite groups this is known as Clifford theory. $\endgroup$
    – Bruce Westbury
    Commented Jul 18, 2012 at 9:22

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