We report the measurement of the absolute d(36) nonlinear coefficient of silver gallium sulfide (AgGaS2) from three phase-matched nonlinear interactions spanning from 10.2 to 0.78 mu m: the sum-frequency of a CO2 laser (10.2 mu m) and a near-IR AlGaAs diode laser (0.842 mu m), the second-harmonic generation of a KCl:Li color-center laser (2.53 mu m), and the noncritically phase-matched 3 omega - omega --> 2 omega difference frequency between the AlGaAs diode laser and the KCI:Li laser to generate 1.265 mu m. From the theoretical evaluation of the Gaussian-beam aperture functions for these type I interactions with arbitrary focusing parameters, beam-waist locations, and absorption losses, we have deduced from the three processes the same consistent value d(36) = 13 (+/- 2) pm/V for AgGaS2. Our value is independent of the growth origin of the material. In light of the trustworthy value of d(36) measured from our experiments we analyze the feasibility of a continuous-wave doubly resonant parametric oscillator-(DRO-)based 3:1 frequency divider pumped by a near-IR diode laser. The predicted pump power threshold for the ring-resonator DRO lies in the range of 70-140 mW for a 14-18mm-long sample with an absorption loss near the level of 1% cm(-1) at the output frequencies. (C) 1997 Optical Society of America.