I'm looking for a group $G$ that is not nilpotent but has a nilpotent Frattini quotient $G/\Phi(G)$. Such a group would have to be necessarily infinite.
Looking for example of a group
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group-theory
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2I think it's also true in the Grigorchuk group. The maximal subgroups all have index 2, and $G/\Phi(G)$ is elementary abelian of order 8. – 2012-12-03