  We study an extension of the gauge group SU(3)_c X SU(2)_L X U(1)_Y of the
standard model to the symmetry group SU(3)_c X SU(4)_L X U(1)_X (3-4-1 for
short). This extension provides an interesting attempt to answer the question
of family replication in the sense that models for the electroweak interaction
can be constructed so that anomaly cancellation is achieved by an interplay
between generations, all of them under the condition that the number of
families must be divisible by the number of colours of SU(3)_c. This method of
anomaly cancellation requires a family of quarks transforming differently from
the other two, thus leading to tree-level flavour changing neutral currents
(FCNC) transmitted by the two extra neutral gauge bosons $Z'$ and $Z''$
predicted by the model. In a version of the 3-4-1 extension, which does not
contain particles with exotic electric charges, we study the fermion mass
spectrum and some aspects of the phenomenology of the neutral gauge boson
sector. In particular, we impose limits on the $Z-Z'$ mixing angle and on the
mass scale of the corresponding physical new neutral gauge boson $Z_2$, and
establish a lower bound on the mass of the additional new neutral gauge boson
$Z'' \equiv Z_3$. For the analysis we use updated precision electroweak data at
the Z-pole from the CERN LEP and SLAC Linear Collider, and atomic parity
violation data. The mass scale of the additional new neutral gauge boson $Z_3$
is constrained by using updated experimental inputs from neutral meson mixing
in the analysis of the sources of FCNC in the model. The data constrain the
$Z-Z'$ mixing angle to a very small value of O(0.001), and the lower bounds on
$M_{Z_2}$ and on $M_{Z_3}$ are found to be of O(1 TeV) and of O(7 TeV),
repectively.
