Conjugacy Class of Element of Center is Singleton/Corollary

Corollary to Conjugacy Classes of Center Elements are Singletons
Let $G$ be a group.

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

The number of single-element conjugacy classes of $G$ is the order of $Z \left({G}\right)$ and divides $\left|{G}\right|$.

Proof
From Conjugacy Classes of Center Elements are Singletons, each of the singleton conjugacy classes consists of one of the elements of $Z \left({G}\right)$.

By Center is Subgroup, $Z \left({G}\right)$ is a subgroup of $G$.

It follows from Lagrange's Theorem that the number of these divides the order of $G$.