 Solution (source code)

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= Solution

The <Sylow theorems> state that if $|G|=p^am$ with $p\nmid m$, then:

* $G$ has a <Sylow subgroup> of order $p^a$;
* every $p$-subgroup is contained in a Sylow $p$-subgroup;
* all Sylow $p$-subgroups are conjugate;
* their number $n_p$ satisfies $n_p\mid m$ and $n_p\equiv1\pmod p$.

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