Definition:Dicyclic Group/Quaternion Group

Definition
The dicyclic group $\Dic 2$ is known as the quaternion group.

The elements of $\Dic 2$ are:
 * $\Dic 2 = \set {e, a, a^2, a^3, b, a b, a^2 b, a^3 b}$

Its group presentation is given by:
 * $\Dic 2 = \gen {a, b: a^4 = e, b^2 = a^2, a b a = b}$

Cayley Table
Its Cayley table is given by:

Also known as
Many sources (including this website) tend to refer to this group merely as $Q$.

Also see

 * Quaternion Group is Hamiltonian