General affine group:GA(1,5)

Definition
This group is defined in the following equivalent ways:


 * 1) It is the member of family::general affine group of degree one over the field of five elements. In other words, it is the semidirect product of the additive and multiplicative groups of this field. It is denoted $$GA(1,5)$$.
 * 2) It is the holomorph of the cyclic group of order five.
 * 3) It is the member of family::Suzuki group $$Sz(2)$$ or the Suzuki group $$Sz(2^{1 + 2m})$$ where $$m = 0$$. Note: This is the only non-simple Suzuki group.

The group can be given by the presentation, with $$e$$ denoting the identity element:

$$\langle a,b \mid a^5 = b^4 = e, bab^{-1} = a^2 \rangle$$