Let $G$ be a finite group. Let $\pi(G)=\{2,3,5\}$ be the set of prime divisors of its order of $G$. If 6 divide the number of Sylow 5subgroups of $G$ and 10 divide the number of Sylow 3subgroups of $G$, then whether the group $G$ group with those properties is unsolvable? Thank you so much.
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closed as too localized by Felipe Voloch, Chandan Singh Dalawat, Andres Caicedo, Anthony Quas, Chris Godsil Jun 16 '12 at 17:23
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