Semidirect product of Z8 and Z8 of semidihedral type

Definition
This group is defined by the following presentation:

$$\! \langle G := \langle a,b \mid a^8 = b^8 = e, bab^{-1} = a^3\rangle$$

Here, $$e$$ denotes the identity element.

Description by presentation
gap> F := FreeGroup(2);  gap> G := F/[F.1^8,F.2^8,F.2*F.1*F.2^(-1)*F.1^(-3)];  gap> IdGroup(G); [ 64, 15 ]