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My mind is a little foggy right now, so I would like to ask for some help on this (or an appropriate reference). Suppose $A$ is an elementary abelian $p$-group and $B$ is a cyclic group of order coprime to $p$. Assume also that $B$ acts fixed-point-freely on $A$. My question then is: does this situation yield any immediate structural information about their semi-direct product $\Gamma=A\rtimes B$? For example, in terms of conjugacy classes, or the subgroup lattice of $\Gamma$?

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