Generalized quaternion group

Definition
A generalized quaternion group is a group of order $$2^{k+1}$$ with generators $$x$$ and $$a$$ such that the group has the presentation:

$$$$

Equivalently, it is the dicyclic group with parameter $$2^{k-1}$$.

For the particular case $$k=2$$, we recover the quaternion group.