Conjugacy class

Given an element $g$ of a Group $G$, the conjugacy class of $g$ in $G$ is $\{ x g x^{-1} : x \in G \}$. It is the collection of elements to which $g$ is conjugate.

[todo: examples] [todo: class equation] [todo: it is the stabiliser of a certain action, which we can show conditionally on the right requisites]