M32

Definition
The group is the semidirect product of the cyclic group of order sixteen and cyclic group of order two, where the latter acts by the $$9^{th}$$ power map:

$$G := \langle a,x \mid a^{16} = x^2 = e, xax = a^9 \rangle$$.

Other descriptions
This group can be constructed using its presentation:

gap> F := FreeGroup(2);  gap> G := F/[F.1^(16), F.2^2, F.2 * F.1 * F.2^(-1) * F.1^7]; 