C-groups of high rank for the symmetric groups

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We classify C-groups of ranks n-1 and n-2 for the symmetric group Sₙ. We also show that all these C-groups correspond to 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.