In mathematical finite group theory, a rank 3 permutation group is a group acting transitively on a set such that the stabilizer of a point has 3 orbits. The study of these groups was started by . Several of the sporadic simple groups were discovered as rank 3 permutation groups.

Classification

The primitive rank 3 permutation groups are all in one of the following classes:
classified the ones such that where the socle

Socle (mathematics)

-Socle of a group:In the context of group theory, the socle of a group G, denoted Soc, is the subgroup generated by the minimal non-trivial normal subgroups of G. The socle is a direct product of minimal normal subgroups...

T of T₀ is simple, and T₀ is a 2-transitive group of degree √n. classified the ones with a regular elementary abelian normal subgroup classified the ones whose socle is a simple alternating group classified the ones whose socle is a simple classical group classified the ones whose socle is a simple exceptional or sporadic group