Where do I start in such problem? $1965=3\times 131\times 5.$

I think was able to show $n_3=1$ so $S_3$ is normal and G is not simple. $n_{131}=1$ What else can I do there? Should I split in the abelian and non-abelian cases or something like it? Should I use that to show that G is abelian somehow? Would you know where I can find similar exercises?

Thank you for your time and patience.

  • 5
    $\begingroup$ Since $S_3$ and $S_{131}$ are both normal, and intersect trivially, the subgroup they generate is isomorphic to $S_3\times S_{131}$. What is that isomorphic to? $\endgroup$ – Arturo Magidin Nov 5 '19 at 22:05

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