 Conjugacy classes in the affine semidirect product of orders eleven and five

This group has seven conjugacy classes: the identity; two classes of five nonidentity translations, distinguished by square class of the translation parameter; and, for each of the four $r\in Q\setminus \{1\}$, one class $\{(r,b):b\in {\mathbb{F}}_{11}\}$ of size eleven.