We construct a few supercharacter theories for finite semidirect products with the normal subgroup of algebra group type. In the case of algebra groups, these supercharacter theories coincide with the one of P.Diaconis and I.M.Isaaks. For the parabolic subgroups of $GL(n)$, the supercharacters and superclasses are classified.

中文翻译：

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代数群扩展的超字符理论

我们构造了一些具有代数群类型正规子群的有限半直积的超字符理论。在代数群的情况下，这些超字符理论与 P.Diaconis 和 IMIsaaks 之一相吻合。对于$GL(n)$的抛物线子群，对超字符和超类进行分类。