Semidirect product of Z8 and Z4 of M-type

Definition
This group can be defined with the presentation:

$$\langle a,b \mid a^8 = b^4 = e, bab^{-1} = a^5 \rangle$$

Description by presentation
The following code can be used to define the group by means of a presentation:

gap> F := FreeGroup(2);  gap> G := F/[F.1^8,F.2^4,F.2*F.1*F.2^(-1)*F.1^(-5)]; 