Non-Abelian Order 8 Group with One Order 2 Element is Quaternion Group

Theorem
Let $G$ be a group with the following properties:


 * $(1): \quad G$ is non-abelian.


 * $(2): \quad G$ is of order $8$.


 * $(3): \quad G$ has precisely one element of order $2$.

Then $G$ is isomorphic to the quaternion group $Q$.