An extension of the standard model to the local gauge group ${\mathrm{SU}(3)}_{c}\ensuremath{\bigotimes}{\mathrm{SU}(3)}_{L}\ensuremath{\bigotimes}{U(1)}_{X}$ which is a subgroup of the electroweak-strong unification group ${E}_{6}$ is analyzed. The mass scales, the gauge boson masses, and the masses for the spin-1/2 particles in the model are calculated. The mass differences between the up and down quark sectors, between the quarks and leptons, and between the charged and neutral leptons in one family are explained as a consequence of mixing of the ordinary with exotic fermions implied by the model. By using experimental results we constrain the mixing angle between the two neutral currents and the mass of the additional neutral gauge boson to be $\ensuremath{-}0.0015<~\mathrm{sin}\ensuremath{\theta}<~0.0048$ and ${M}_{{Z}_{2}}>~600\mathrm{GeV}$ at 95% C.L. The existence of a Dirac neutrino for each family with a mass of the order of the electroweak mass scale is predicted.