What is the discrete gauge symmetry of the minimal supersymmetric standard model

We systematically study the extension of the supersymmetric standard model (SSM) by an anomaly-free discrete gauge symmetry Z(N). We extend the work of Ibanez and Ross with N=2, 3 to arbitrary values of N. As new fundamental symmetries, we find four Z(6), nine Z(9), and nine Z(18). We then place three phenomenological demands upon the low-energy effective SSM: (i) the presence of the mu term in the superpotential, (ii) baryon-number conservation up to dimension-five operators, and (iii) the presence of the seesaw neutrino mass term LHuLHu. We are then left with only two anomaly-free discrete gauge symmetries: baryon triality, B-3, and a new Z(6), which we call proton hexality, P-6. Unlike B-3, P-6 prohibits the dimension-four lepton-number violating operators. This we propose as the discrete gauge symmetry of the minimal SSM, instead of R parity.