Symmetric Group on 3 Letters/Group Presentation

Group Presentation of Symmetric Group on $3$ Letters
The group presentation of the symmetric group on $3$ letters is given by:
 * $S_3 := \gen {a, b: a^3 = b^2 = \paren {a b}^2 = e}$

Hence:
 * $\begin{array}{c|cccccc}

& e & a & a^2 & b & a b & a^2 b \\ \hline e & e & a & a^2 & b & a b & a^2 b \\ a & a & a^2 & e & a b & a^2 b & b \\ a^2 & a^2 & e & a & a^2 b & b & a b \\ b & b & a^2 b & a b & e & a^2 & a \\ a b & a b & b & a^2 b & a & e & a^2 \\ a^2 b & a^2 b & a b & b & a^2 & a & e \\ \end{array}$