Suzuki group of Lie type ($Sz(q)={}^2{B}_2(q),q=2^{2a+1}\ge 8$)

These simple groups have order $q^2(q^2+1)(q-1)$ and a two-transitive action on a Suzuki ovoid of $q^2+1$ points. The point-stabilizer root group is regular on the remaining points.