  Let G be a unipotent algebraic group over an algebraically closed field k of
characteristic p > 0 and let l be a prime different from p. Let e be a minimal
idempotent in D_G(G), the braided monoidal category of G-equivariant (under
conjugation action) \bar{Q_l}-complexes on G. We can associate to G and e a
modular category M_{G,e}. In this article, we prove that the modular categories
that arise in this way from unipotent groups are precisely those in the class
C_p^{\pm}.
