  We construct a realistic Supersymmetric Grand Unified Theory of Flavour based
on PSL(2,7) x SO(10), where the quarks and leptons in the 16 of SO(10) are
assigned to the complex triplet representation of PSL(2,7), while the flavons
are assigned to a combination of sextets and anti-triplets of PSL(2,7). Using a
D-term vacuum alignment mechanism, we require the flavon sextets of PSL(2,7) to
be aligned along the 3-3 direction leading to the third family Yukawa
couplings, while the flavon anti-triplets describe the remaining Yukawa
couplings. Other sextets are aligned along the neutrino flavour symmetry
preserving directions leading to tri-bimaximal neutrino mixing via a type II
see-saw mechanism, with predictions for neutrinoless double beta decay and
cosmology.
