Normal Supercharacter Theories Of The Dicyclic Groups

Abstract

The supercharacter theory was developed by P. Diaconis and I. M. Isaacs as a natural generalization of the classical ordinary character theory. There are different constructions for finding the supercharacter theories of a finite group. Supercharacter theories of many finite groups, such as cyclic groups, Frobenius groups, dihedral groups, elementary abelian $p$-groups, and Camina groups, etc. are studied with different constructions. One of the constructions uses normal subgroups. In this paper, we consider dicyclic groups and find some of their normal supercharacter theories and some automorphic supercharacter theories in special cases.