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A capital S with a subscript, the group of all rearrangements of that many things.
Also known as: Symmetric group, Permutation group, S n
S_n is every possible way of shuffling n objects, and it has n factorial elements — which grows fast enough that S_5 already has 120. Cayley's theorem says every finite group sits inside one of these, which makes the family the universal container of finite group theory.
Denotes the symmetric group on a given number of letters: the group of all permutations of that set.
Contexts: Mathematics
Has order n factorial, and by Cayley's theorem contains an isomorphic copy of every group of order n.
Contexts: Mathematics
A capital letter S with a small numeral set below and to the right.