  We introduce the notion of vertex operator superalgebra with enhanced
conformal structure, which is a refinement of the notion of vertex operator
superalgebra. We exhibit several examples, including a particular one which is
self-dual, and whose full symmetry group is a direct product of a cyclic group
of order seven with the sporadic simple group of Rudvalis. We thus obtain an
analogue of Monstrous Moonshine for a sporadic group not involved in the
Monster. Two variable analogues of the usual McKay--Thompson series are
naturally associated to the action of the Rudvalis group on this object, and we
provide explicit expressions for all the series arising.
