Finite permutation groups of rank 3

By the rank of a transitive permutation group we mean the number of orbits of the stabilizer of a point thus rank 2 means multiple transitivity. Interest is drawn to the simply transitive groups of "small" rank > 2 by the fact that every known finite simple group admits a representation as a primitive group of rank at most 5 while not all of these groups have doubly transitive representations. In this paper we consider finite transitive groups of rank 3, a class of groups which seems to have received little direct attention.