Symmetric Group on 3 Letters/Center

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

The center of $S_3$ is given by:
 * $\map Z {S_3} = \set e$

Proof
From Center of Dihedral Group:
 * $\map Z {D_n} = \begin{cases} e & : n \text { odd} \\ \set {e, \alpha^{n / 2} } & : n \text { even} \end{cases}$

Hence the result.