Singer cycle
= Singer cycle
{c}
{title2=$C_{q^n-1}\le GL_n(q)$}
Multiplication by a generator of $\mathbb F_{q^n}^{\times}$ on the $\mathbb F_q$-space $\mathbb F_{q^n}$ gives a cyclic subgroup regular on nonzero vectors. Its normalizer contains the field Frobenius automorphism. In degree three over $\mathbb F_2$ the full normalizer has order 21.