Abstract: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 compu… Show more
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