Conjugacy Class of Element of Center is Singleton

Theorem
Let $G$ be a group.

Let $Z \left({G}\right)$ be the center of $G$.

The elements of $Z \left({G}\right)$ form singleton conjugacy classes, and the elements of $G \setminus Z \left({G}\right)$ belong to multi-element conjugacy classes.

Proof
Let $\mathrm C_a$ be the conjugacy class of $a$ in $G$.