We perform a multi-band statistical analysis of core-dominated superluminal active galactic nuclei (AGN) detected with Fermi Large Area Telescope (LAT). The detection rate of $gamma$-ray jets is found to be high for optically bright AGN. There is a significant correlation between the $gamma$-ray luminosity and the optical nuclear and radio (15 GHz) luminosities of AGN. We report a well defined positive correlation between the $gamma$-ray luminosity and the radio-loudness for quasars and BL Lacertae type objects (BL Lacs). The slope of the best-fit line is significantly different for quasars and BL Lacs. The relations between the optical and radio luminosities and the $gamma$-ray loudness are also examined, showing a different behavior for the populations of quasars and BL Lacs. Statistical results suggest that the $gamma$-ray, optical and radio emission is generated at different locations and velocity regimes along the parsec-scale jet.
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