Trivial examples for the first condition are easy to find: $G={1},C_2$.
Are there any (finite\non-finite) groups that satisfy the conditions in the title?
2026-04-13 10:43:08.1776076988
Are there groups $G$ isomorphic to $\mathrm{Aut}\left( \mathrm{Aut} (G)\right)$, such that $G\not\cong \mathrm{Aut}(G)$?
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