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.

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