Nontrivial semidirect product of Z4 and Z8

Definition
This group is defined by the presentation:

$$\! G := \langle a,b \mid a^4 = b^8 = e, bab^{-1} = a^3 \rangle$$

Description by presentation
The group can be described in GAP using its presentation:

gap> F := FreeGroup(2);  gap> G := F/[F.1^4,F.2^8,F.2*F.1*F.2^(-1)*F.1];  gap> IdGroup(G); [ 32, 12 ]