  We design a supersymmetric SU (5) GUT model using \Delta (54), a finite
non-abelian subgroup of SU (3)f . Heavy right handed neutrinos are introduced
which transform as three-dimensional repre-sentation of our chosen family
group. The model successfully reproduces the mass hierarchical mass structures
of the Standard Model, and the CKM mixing matrix. It then provides predictions
for the light neutrino with a normal hierarchy and masses such that m{\nu},1
\approx 5\times10-3 eV, m{\nu}, 2 \approx 1\times 10-2 eV, and m{\nu},3 \approx
5 \times 10-2 eV. We also provide predictions for masses of the heavy
neutrinos, and correc- tions to the tri-bimaximal matrix that fit within
experimental limits, e.g. a reactor angle of -7.31o. A simple modification to
our model is introduced at the end and is shown to also produce predictions
that fall well within those limits.
