Affine semidirect product of cyclic groups of orders eleven and five
= Affine semidirect product of cyclic groups of orders eleven and five
Let $Q$ be the subgroup of nonzero squares in $\mathbb F_{11}^\times$. The affine maps
$$
x\longmapsto rx+b,
\qquad r\in Q,\quad b\in\mathbb F_{11},
$$
form the nonabelian semidirect product $C_{11}\rtimes C_5$, with multiplication
$$
(r,b)(s,c)=(rs,b+rc).
$$