Because SHG is a second-order process, standard heuristics dictate that it will be brighter than third-order processes such as THG. However, the observed SHG intensity in all cases herein is at least an order of magnitude less than the THG intensity (ratios tabulated in Table for the specific case of ω = 1.03 eV). In the SI we discuss and rule out various reasons why I THG I SHG and conclude that SHG is weaker than THG because the anharmonic potential felt by the optically driven electrons is only weakly noncentrosymmetric.