Direct product of M32 and Z2

Definition
This group is defined as the external direct product of defining ingredient::M32 and defining ingredient::cyclic group:Z2. It can also be defined by the following presentation:

$$\langle a,b,c \mid a^{16} = b^2 = c^2 = e, bab^{-1} = a^9, ac = ca, bc = cb \rangle$$