# Dihedral Group D3/Cayley Table

## Cayley Table of Dihedral Group $D_3$
The Cayley table of the dihedral group $D_3$ can be written:
$\begin{array}{c|cccccc} & e & a & a^2 & b & a b & a^2 b \\ \hline e & e & a & a^2 & b & a b & a^2 b \\ a & a & a^2 & e & a b & a^2 b & b \\ a^2 & a^2 & e & a & a^2 b & b & a b \\ b & b & a^2 b & a b & e & a^2 & a \\ a b & a b & b & a^2 b & a & e & a^2 \\ a^2 b & a^2 b & a b & b & a^2 & a & e \\ \end{array}$
where the group presentation of $D_3$ is given as:
$D_3 = \gen {a, b: a^3 = b^2 = e, a b = b a^{-1} }$