  We propose a Pati-Salam extension of the standard model incorporating a
flavor symmetry based on the $\Delta \left( 27\right)$ group. The theory
realizes a realistic Froggatt-Nielsen picture of quark mixing and a predictive
pattern of neutrino oscillations. We find that, for normal neutrino mass
ordering, the atmospheric angle must lie in the higher octant, CP must be
violated in oscillations, and there is a lower bound for the $0\nu\beta\beta$
decay rate. For the case of inverted mass ordering, we find that the lower
atmospheric octant is preferred, and that CP can be conserved in oscillations.
Neutrino masses arise from a low-scale seesaw mechanism, whose messengers can
be produced by a $Z^{\prime }$ portal at the LHC.
