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or divides order of G/Frattini(G)? G is nilpotent ?

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 No, the size of the conjugacy class of 1 is 1 and divides everything. Voted to close as not a real uestion. – Mark Sapir Sep 2 at 11:59
let G is finite group, and every size squared of conjugacy class divides the order of G/Z(G), then,G is Nilpotent? – ANGELABABY Sep 3 at 1:13

closed as not a real question by Mark Sapir, Noah Snyder, Lee Mosher, Steven Landsburg, Alex Bartel Sep 2 at 18:55

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