Definition:Conjugacy Class

Definition
The equivalence classes into which the conjugacy relation divides its group into are called conjugacy classes.

The conjugacy class of an element $x \in G$ can be denoted $\operatorname{C}_x$.

Some authors use the notation $\operatorname{cl} \left({x}\right)$, but this can be confused with the notation for closure in the context of topology, so its use is not recommended.