C-groups of high rank for the symmetric groups.

We give presentations for the C-groups of rank n − 1 of the symmetric group S n . We also classify C-groups of rank n − 2 for S n . We show that all these C-groups correspond to regular hypertopes, that is, thin, residually connected flag-transitive geometries. Therefore we generalise some similar results obtained in the framework of string C-groups that are in one-to-one correspondence with abstract regular polytopes. [ABSTRACT FROM AUTHOR]