  The theory of topological modular forms (TMF) predicts that elliptic genera
of physical theories satisfy a certain divisibility property, determined by the
theory's gravitational anomaly. In this note we verify this prediction in
Duncan's Supermoonshine module, as well as in tensor products and orbifolds
thereof. Along the way we develop machinery for computing the elliptic genera
of general alternating orbifolds and discuss the relation of this construction
to the elusive "periodicity class" of TMF.
