  We consider two generalizations of the N=6 superconformal Chern-Simons-matter
theories with gauge group U(N)xU(N). The first generalization is to N=6
superconformal U(M)xU(N) theories, and the second to N=5 superconformal
O(2M)xUSp(2N) and O(2M+1)xUSp(2N) theories. These theories are conjectured to
describe M2-branes probing C^4/Z_k in the unitary case, and C^4/\hat{D}_k in
the orthogonal/symplectic case, together with a discrete flux, which can be
interpreted as |M-N| fractional M2-branes localized at the orbifold
singularity. The classical theories with these gauge groups have been
constructed before; in this paper we focus on some quantum aspects of these
theories, and on a detailed description of their M theory and type IIA string
theory duals.
