  We perform a complete calculation at the one-loop level for the Zggg and
Z'ggg couplings in the context of the minimal 331 model, which predicts the
existence of a new Z' gauge boson and new exotic quarks. Bose symmetry is
exploited to write a compact and manifest SU_C(3)-invariant vertex function for
the Vggg (V=Z,Z') coupling. Previous results on the $Z\to ggg$ decay in the
standard model are reproduced. It is found that this decay is insensitive to
the effects of the new exotic quarks. This in contrast with the $Z'\to ggg$
decay, which is sensitive to both the standard model and exotic quarks, whose
branching ratio is larger than that of the $Z\to ggg$ transition by about a
factor of 4.
