Character groups of Metacyclic groups

Pontryagin duality provides a powerful tool for analyzing the structure and properties of locally compact abelian groups, in particular finite abelian groups. Now much can be done with non-abelian groups via the construction of character groups. In this paper we provide a set of conditions a group must satisfy to be realized as a balanced character group for a metacyclic group. Furthermore we provide a classification for the balanced character groups of a particular class of metacyclic groups, the dicyclic groups.