The nonlinear optical properties, IR and Raman frequencies as well as NMR chemical shifts of two S6 symmetrical C48N12 azafullerene isomers (I and II conformations) were calculated and compared with those of C60 at the B3LYP/6-31G* level of density functional theory. The second order hyperpolarizabilities were determined by means of ZINDO/SOS. The static (hyper)polarizabilities of C48N12 are smaller than those of C60, whereas the DC-electric field induced second harmonic generation of II is 58% larger than that of C60 at the frequency of 1.1653 eV, suggesting that II is a potential NLO candidate. In contrast to I, all five of the most intense IR and Raman frequencies of II exceed 1000 cm−1. These differences, and those between the computed 13C NMR chemical shifts of I and II should be useful to distinguish and to identify these two structural isomers.