Symmetric Group on 3 Letters

Definition
Let $S_3$ denote the set of permutations on $3$ letters.

The symmetric group on $3$ letters is the algebraic structure:
 * $\paren {S_3, \circ}$

where $\circ$ denotes composition of mappings.

It is usually denoted, when the context is clear, without the operator: $S_3$.

Also see

 * Symmetric Group is Group, which demonstrates that this is a (finite) group.