  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.
