Abstract

We describe an easy way how to find supercharacter theories for a finite group, if its character table is known. Namely, we show how an arbitrary partition of the conjugacy classes or of the irreducible characters 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.

中文翻译：

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在字符表上查找超级字符理论

摘要

我们描述了一种简单的方法，如果已知其字符表，则该方法如何为有限组查找超级字符理论。即，我们展示了如何将共轭类或不可约字符的任意分区提炼为属于超级字符理论的最粗糙分区。我们的构造强调超类和超级字符之间的对偶。提出了一种在给定字符表上查找所有超级字符理论的算法。该算法用于计算具有多达26个共轭类的某些非阿贝尔简单群的超级字符理论的数量。