An array of low-symmetry, L-shaped gold nanoparticles is shown to exhibit high sensitivity to the state of incident polarization. Small imperfections in the shape of the actual particles, including asymmetric arm lengths and edge distortions, break the symmetry attributed to an ideal particle. This broken symmetry leads to a large angular displacement of the extinction axes from their expected locations. More significantly, second-harmonic generation experiments reveal significant second-order susceptibility tensor components forbidden to the ideal symmetry.