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Describe all semidirect products of $C_n$ by $C_m$ (ie $C_n \rtimes C_m$) where $m,n \in \mathbb{N_+}$

Note: For the first attempt one needs to find all homomorphisms from $C_m \to U(n)$, but the situation differs a lot for different pairs of $n ,m$, is there a better way to find all structures of $C_n \rtimes C_m$?

Wikipedia provided a general presentation of this product which I do not know how it was worked out.

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    Thanks! It's clear to me now. the phi(y) is in$U(n)$thus coprime to$n$which is equal to the symbol "k" in the presentaion given by the wiki site above.2012-05-31

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