Projective special unitary group over a finite field
= Projective special unitary group over a finite field
{title2=$PSU_n(q)$}
The projective quotient of determinant-one matrices preserving a nondegenerate Hermitian form over $\mathbb F_{q^2}$, with conjugation $x\mapsto x^q$. In dimension three its natural two-transitive action has $q^3+1$ isotropic points. For $q\ge3$ its order is $q^3(q^3+1)(q^2-1)/\gcd(3,q+1)$.