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For which finite groups $G$ is $\operatorname{Aut}(G)$ isomorphic to a (non necessarily strict) subgroup of $G$?

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  • $\begingroup$ Do you known any interesting examples? $\endgroup$ – lhf Mar 24 at 23:05
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    $\begingroup$ $Aut(C_{2})$ is trivial, $Aut(S_{3})\cong S_{3}$. $\endgroup$ – Sylvain Julien Mar 25 at 6:02