Symmetric Group on 3 Letters/Conjugacy Classes

Conjugacy Classes of the Symmetric Group on 3 Letters
Let $S_3$ denote the Symmetric Group on 3 Letters, whose Cayley table is given as:

The conjugacy classes of $S_3$ are:
 * $\set e, \set {\tuple {123}, \tuple {132} }, \set {\tuple {12}, \tuple {13}, \tuple {23} }$