  Color-ordered amplitudes for the scattering of n particles in the adjoint
representation of SU(N) gauge theory satisfy constraints that arise from group
theory alone. These constraints break into subsets associated with irreducible
representations of the symmetric group S_n, which allows them to be presented
in a compact and natural way. Using an iterative approach, we derive the
constraints for six-point amplitudes at all loop orders, extending earlier
results for n=4 and n=5. We then decompose the four-, five-, and six-point
group-theory constraints into their irreducible S_n subspaces. We comment
briefly on higher-point two-loop amplitudes.
