Generalized quaternion group:Q32

Definition
This group is the generalized quaternion group of order $$32$$, or the dicyclic group of degree $$8$$. It has the presentation:

$$G = \langle a,b,c \mid a^8 = b^2 = c^2 = abc \rangle$$.

Other descriptions
The group can be described using its presentation:

gap> F := FreeGroup(3);  gap> G := F/[F.1^8 * F.2^(-2), F.2^2 * F.3^(-2), F.1 * F.2 * F.3^(-1)]; 