  We compute and tabulate the Clesbsch--Gordan coefficients of the $SU(6)
\supset SU(3) \times SU(2)$ product ${\overline{\bf 56}} \otimes {\bf 56}$,
which are relevant to the nonrelativistic spin-flavor symmetry of the lightest
baryons. Under the assumption that the largest representation in this product,
the ${\bf 2695}$, gives rise to operators in a chiral expansion that produce
numerically small effects, we obtain a set of relations among the masses of the
baryons, as well as among their magnetic dipole and higher multipole moments.
We compare the mass relations to experiment, and find numerical predictions for
the $\Sigma^0$-$\Lambda$ mass mixing parameter and eighteen of the twenty-seven
magnetic moments in the ${\bf 56}$.
