  We present a method to generate all fusion rings of a specific rank and
multiplicity. This method was used to generate exhaustive lists of fusion rings
up to order 9 for several multiplicities. We introduce a class of
non-commutative fusion rings based on a group with transitive action on a set.
This generalizes the Tambara-Yamagami (TY) and Haagerup- Izumi (HI) fusion
rings. We give an example of such a ring which is categorifiable and is not of
TY or HI type. The structure of non-commutative fusion rings with a subgroup is
reviewed, and the one-and two-particle extensions of groups are classified. A
website containing data on fusion rings is introduced, and an overview of a
Wolfram Language package for working with these rings is given.
