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Conjugacy Classes, Class Equation: Dihedral Group with 6 Elements


Let $D_3$ be the dihedral group with six elements, and with neutral element $e$.

It has presentation: $D_3=\langle a,b\mid a^3=b^2=e, aba=b^{-1}\rangle$.

For any $g\in D_3$, let $\operatorname{C}_g$ be the conjugacy class of $g$ in $D_3$.

The group $D_3$ is the disjoint union of

. One way to write the Class Equation for $D_3$ is