Normal supercharacter theory of the dihedral groups

Abstract

Diaconis ‎and ‎Isaacs ‎defined ‎the ‎‎supercharacter ‎theory ‎for ‎finite ‎groups ‎as a‎ ‎natural ‎generalization ‎of ‎the ‎classical ‎ordinary ‎character ‎theory ‎of ‎finite ‎groups. ‎‎Supercharacter ‎theory ‎of ‎many ‎finite ‎groups ‎such ‎as ‎the ‎cyclic ‎groups, ‎the ‎Frobenius ‎groups, ‎etc. ‎were ‎well ‎studied ‎and ‎well-known. ‎In ‎this ‎paper ‎we ‎find ‎the ‎normal ‎and ‎automorphic ‎‎supercharacter ‎theories ‎of ‎the ‎dihedral ‎groups ‎in ‎special ‎cases.‎

Keywords

• dihedral group
• ‎ supercharacter
• superclass
• lattice of normal subgroups