  One way of expressing the self-duality $A\cong \Hom(A,\mathbb{C})$ of Abelian
groups is that their character tables are self-transpose (in a suitable
ordering). Noncommutative groups fail to satisfy this property. In this paper
we extend the duality to some noncommutative groups considering when the
character table of a finite group is close to being the transpose of the
character table for some other group. We find that groups dual to each other
have dual normal subgroup lattices. We show that our concept of duality cannot
work for non-nilpotent groups and we describe $p$-group examples.
