  We present explicit formulas for the matrix elements of the SU(6) generators
for totally symmetric spin-flavor states, relevant for baryon spectroscopy in
large $N_c$ QCD. We rely on the interplay between two different methods to
calculate these matrix elements. As an outcome, general analytic formulas of
the corresponding SU(6) isoscalar factors are derived for arbitrary $N_c$.
These results can be used to study excited states of nonstrange and strange
baryons.
