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Wikipedia definition
1. Symmetric groupIn mathematics, the symmetric group Sn on a finite set of n symbols is the group whose elements are all the permutations of the n symbols, and whose group operation is the composition of such permutations, which are treated as bijective functions from the set of symbols to itself. Since there are n! possible permutations of a set of n symbols, it follows that the order (the number of elements) of the symmetric group Sn is n!.
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