 Solution (source code)

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= Solution

Write $|G|=p^nm$ with $p\nmid m$. The <Sylow theorems> state:

* $G$ has a subgroup of order $p^n$.
* Every $p$-subgroup lies in a Sylow $p$-subgroup, and all Sylow $p$-subgroups are conjugate.
* Their number $n_p$ satisfies $n_p\equiv1\pmod p$ and $n_p\mid m$.

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