M64

Definition
This group, denoted $$M_{64}$$, is defined as the semidirect product of defining ingredient::cyclic group:Z32 by defining ingredient::cyclic group:Z2 where the latter acts on the former by the $$17^{th}$$ power map. Explicitly, it has the following presentation:

$$G := \langle a,b \mid a^{32} = b^2 = e, bab^{-1} = a^{17}\rangle$$