  First, I construct an isomorphism between the categories of (topological)
groups of nilpotency class 2 with 2-divisible center and (topological) Lie
rings of nilpotency class 2 with 2-divisible center. That isomorphism allows us
to construct adjoint and coadjoint representations as usual. For a finite group
G of nilpotency class 2 of odd order, I construct a basis in its group algebra
C[G], parameterized by elements of g* so that the elements of coadjoint orbits
form bases of simple two-side ideals of C[G]. That construction gives us a
one-to-one correspondence between G-orbits in g* and classes of equivalence of
irreducible unitary representations of G, implying a very simple character
formula. The properties of that correspondence are similar to the properties of
the analogous correspondence given by Kirillov's orbit method for nilpotent
connected and simply connected Lie groups. The diagram method introduced in my
article 'Diagrams of Representations, math.RT/9803079 (1998)' and my thesis 'A
Combinatorial Approach to Representations of Lie Groups and Algebras,
University of Pennsylvania (1998)' gives us a convenient way to study normal
forms on the orbits and corresponding representations.
