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Definition (Conjugacy Class Of A)
Let $G$ be a group. Suppose that $a$ and $b$ are elements of $G$. We say that $a$ and $b$ are conjugate in $G$ if $b=x^{-1}ax$ for some $x\in G$, and we say that $b$ is a conjugate of $a$. The set of conjugates of $a$ is called the conjugacy class of $a$ which we denote by $\text{cl}(a)=\{x^{-1}ax\mid x\in G\}$.
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