Show that the possible orders of the elements of group $S_{7}$ part of the set $\{1,2,3,4,5,6,7,10,12\}$
2026-04-07 14:39:18.1775572758
The possible element orders of $S_{7}$.
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The possible orders of an element in $S_7$ are least common multiples of the numbers in partitions of $7$. This is because the order of $\sigma\in S_7$ is equal to the least common multiple of the lengths of the cycles in its disjoint cycle decomposition.