Unitary t-groups

Relying on the main results of [Guralnick-Tiep], we classify all unitary $t$-groups for $t geq 2$ in any dimension $d geq 2$. We also show that there is essentially a unique unitary $4$-group, which is also a unitary $5$-group, but not a unitary $t$-group for any $t geq 6$.