What is the smallest example of a finite solvable, non-nilpotent group $G$, such that its derived subgroup $G'$ is nilpotent, but not abelian?
2026-02-23 02:23:36.1771813416
Solvable, non-nilpotent group with nilpotent commutator subgroup
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The group $\operatorname{SL}(2,3)$ has order $24$ and derived subgroup isomorphic to the quaternion group of order $8$. You can check that no smaller group meets your requirements.