G-graphs and special representations for binary dihedral groups in GL(2,C)

TL;DR

This paper classifies all G-graphs for small binary dihedral groups in GL(2,C) and describes their special representations using combinatorial methods related to maximal cyclic normal subgroups.

Contribution

It provides a complete classification of G-graphs and a combinatorial description of special representations for binary dihedral groups in GL(2,C).

Findings

Classification of all G-graphs for small binary dihedral groups.

Combinatorial description of special representations.

Connection between representations and maximal cyclic normal subgroups.

Abstract

We give the classification of all possible G-graphs for any small binary dihedral subgroup G in GL(2,C) and use this classification to give the combinatorial description of the special representations of G in terms of its maximal cyclic normal subgroup.