Suzuki groups

These simple groups are the only finite non-abelian ones with orders not divisible by 3.

In the lowest case the symplectic group B2(2)≈S6; its exceptional automorphism fixes the subgroup Sz(2) or 2B2(2), of order 20.

Ono (1962) gave a detailed exposition of Ree's observation.

Tits (1962) constructed the Suzuki groups as the symmetries of a certain ovoid in 3-dimensional projective space over a field of characteristic 2.

Suzuki groups are CN-groups: the centralizer of every non-trivial element is nilpotent.