String C-groups as transitive subgroups of Sym(n)
  If $\Gamma$ is a string C-group which is isomorphic to a transitive subgroup of the symmetric group Sym(n) (other than Sym(n) and the alternating group Alt(n)), then the rank of $\Gamma$ is at most $n/2+1$, with finitely many exceptions (which are classified). It is conjectured that only the symmetric group has to be excluded. 
Peter J. Cameron, Maria Elisa Fernandes, Dimitri Leemans and Mark   Mixer
math.GR