Determining the fusion coefficients for an abstract fusion category is very difficult, and generalizes the problem of plethysm for group representations. As is the case in finite groups, restricting the class of objects we consider can help us to obtain better general results. When one has a group acting on a modular category, it is possible to construct an extension for which the fusion rules are attainable. How does this relate to the study of group characters and extensions? We discuss some generalizations of Abelian group extensions and future work.