The frequency doubling process resulting from the nonlinear interaction of ultrashort laser pulses in nonlinear photonic crystals modulated with second-order nonlinear admittance was studied based on numerical modeling. The effects of linear absorption in the infrared spectral range and third-order group velocity dispersion on the formation of the second harmonic pulse in these crystals were analyzed. The study considered the case where the conditions of quasi-phase matching and group velocity synchronization were simultaneously fulfilled. Under these conditions, the effect of small deviations of the domain size from the optimal value for quasi-phase matching on the efficiency of second harmonic generation was evaluated. The results showed that it is possible to simultaneously ensure the conditions of quasi-phase matching and group velocity synchronization at a wavelength of approximately 1560 nm of the fundamental radiation.