The mechanism of Fano resonance spectrum dip resulting from the system of symmetric metallic multi-nanoparticles-thin film belonging to C3v and C4v is deduced in detail using group theory. Based on previous research achievements, it is verified that there are only four E modes meet with the same irreducible representation in the system of Cnv symmetric multi-particles-thin film, when the linearly polarized light electric field inputs along the multi-particles plane. There are only three local surface plasmon electric dipole moment resonance symmetry modes in the multi-particles plane, and among them, the periphery ring-multiparticles own two, the central particle own one. These results are completely the same with electric dipole moment distribution of Dnh symmetry multiparticles system. The direction of the electric dipolar moments of the rest one is perpendicular to the multi-particles plane although it satisfies the requirement of the same symmetry. In addition, Cnv and Dnh point groups hold the same spectrum linetype, however, there is some redshift or blueshift of spectrum dip (peak) if the thin film base exists. This work can provide some references for designing the optical properties and its extended applications about the system of metallic multi-nanoparticles-thin film.