Embedding phenomenological quark-lepton mass matrices into SU(5) gauge models

We construct phenomenological quark-lepton mass matrices based on an ${\mathrm{S}}_3$ permutation symmetry in a manner fully compatible with SU(5) grand unification. The Higgs particles we need are 5, 45 and their conjugates. The model gives a charge $-1/3$ quark versus a charged-lepton mass relation, and also a good fit to mass-mixing relations for the quark sector, as well as an attractive mixing pattern for the lepton sector, explaining a large mixing angle between ${\nu }_{\mu }$ and ${\nu }_{\tau },$ and either a large or small ${\nu }_e-{\nu }_{\mu }$ mixing angle, depending on the choice of couplings, consistent with the currently accepted solutions to the solar neutrino problem.