# Conjugacy classes in $Q_8$

I know that in the quaternion group $$Q_8$$, there are $$5$$ conjugacy classes, $$2$$ of which are $$\{1\}$$ and $$\{-1\}$$. Why are $$1$$ and $$-1$$ in their own conjugacy classes rather than a single one: $$\{1, -1\}$$? Thanks!

• Because they are both in the center. Observe that $g1g^{-1}=1$ for all $g\in G$ with any group $G$. Hence $1$ is always in a conjugacy class by itself. – Jyrki Lahtonen Apr 13 '17 at 19:52