  We analyze the chiral operator ring of the symmetric orbifold conformal field
theory on the complex two-plane. We compute the large N limit of the ring and
exhibit its factorized leading order behaviour. We moreover calculate all
structure constants at the subleading and sub-subleading order. These features
are coded as properties of the symmetric group and we review the relevant
mathematical theorems on the product of conjugacy classes in the center of the
group algebra. We illustrate the efficiency of the formalism by iteratively
computing broad classes of higher point extremal correlators. We point out
generalizations of our simplest of models and argue that our combinatorial
analysis is relevant to the organization of the large N perturbation theory of
generic symmetric orbifolds.
