Frieder Ladisch
Published 2020-09-28Version 1
We describe an easy way how to find supercharacter theories for a finite group $G$, if the character table of $G$ is known. Namely, we show how an arbitrary partition of the conjugacy classes of $G$ or of the irreducible characters of $G$ can be refined to the coarsest partition that belongs to a supercharacter theory. Our constructions emphasize the duality between superclasses and supercharacters. An algorithm is presented to find all supercharacter theories on a given character table. The algorithm is used to compute the number of supercharacter theories for some nonabelian simple groups with up to 26 conjugacy classes.
Comments: 18 pages, ancillary file with GAP code
Supercharacter theory for groups of invertible elements of reduced algebras
Submatrices of character tables and basic sets
Supercharacter theories for Sylow $p$-subgroups of the Ree groups
![QR code for arXiv:2009.13590 [math.RT]](http://oss.arxitics.com/images/favicon.svg)