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In third quantization the origin of fermion families is easy to understand:the electron field, the muon field and the tau field are identical fields inprecisely the same sense as three electrons are identical and undistinguishableparticles of a theory of second quantization. In both cases, the permutation ofthese fields or particles leaves the lagrangian invariant. One can also extendthe concept of family to gauge bosons. This can be obtained through thesemidirect product of the gauge group with the group of permutations of nobjects. In this paper we have studied the group E_6^4 x S_4. We explain why wehave chosen E_6 as fundamental gauge group factor and why we start with a modelwith four gauge boson/fermion families to accommodate and to fit the standardmodel with only three fermion families. We suggest a possible symmetry breakingpattern of E_6^4 x S_4 that could explain quark, lepton and neutrino masses andmixings.Comment: 21 pages, no figur

GAUGE BOSON FAMILIES IN GRAND UNIFIED THEORIES OF FERMION MASSES: $E_6^4 \rtimes S_4$