String C-groups as transitive subgroups of $S_n$ - Cameron, Peter J. (2018)
If $Γ$ is a string C-group which is isomorphic to a transitive subgroup of the symmetric group Sn (other than Sn and the alternating group An), then the rank of is at most n/2+1, with nitely many exceptions (which are classi ed). It is conjectured that only the symmetric group has to be excluded.