Semidihedral group:SD32

Definition
The group is the member of family::semidihedral group of order $$32$$. In other words, it is defined by the following presentation:

$$G := \langle a,x \mid a^{16} = x^2 = e, xax = a^7 \rangle$$.

Other descriptions
The group can be defined as:

gap> F := FreeGroup(2);  gap> G := F/[F.1^(16), F.2^2, F.2 * F.1 * F.2 * F.1^9]; 

$$G$$ is the semidihedral group of order $$32$$.