Semidirect product of Z5 and Z8 via inverse map

Definition
This group of order 40 can be defined by the following presentation (here, $$e$$ is used for the identity element):

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

Description by presentation
The group can be defined in GAP using its presentation as follows:

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

We can check that this is the correct group:

gap> IdGroup(G); [ 40, 1 ]