How can we find the number of subgroups of order $n$, where $n$ is prime, in the symmetric group $S_n$? Typically, I am interested in, say $S_{17}$. I am stuck at this problem. I think it has something to do with the conjugacy classes of the symmetric group. Any ideas. Thanks beforehand.
2026-04-04 01:54:48.1775267688
number of subgroups of order $ n $ in $S_n$
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