We analyse the Fundamental Plane (FP) relation of $39,993$ early-type galaxies (ETGs) in the optical (griz) and $5,080$ ETGs in the Near-Infrared (YJHK) wavebands, forming an optical$+$NIR sample of $4,589$ galaxies. We focus on the analysis of the FP as a function of the environment where galaxies reside. We characterise the environment using the largest group catalogue, based on 3D data, generated from SDSS at low redshift ($z < 0.1$). We find that the intercept $``c$ of the FP decreases smoothly from high to low density regions, implying that galaxies at low density have on average lower mass-to-light ratios than their high-density counterparts. The $``c$ also decreases as a function of the mean characteristic mass of the parent galaxy group. However, this trend is weak and completely accounted for by the variation of $``c$ with local density. The variation of the FP offset is the same in all wavebands, implying that ETGs at low density have younger luminosity-weighted ages than cluster galaxies, consistent with the expectations of semi-analytical models of galaxy formation. We measure an age variation of $sim 0.048$~dex ($sim 11%$) per decade of local galaxy density. This implies an age difference of about $32 %$ ($sim 3 , Gyr$) between galaxies in the regions of highest density and the field. We find the metallicity decreasing, at $sim 2$~$sigma$, from low to high density. We also find $2.5 , sigma$ evidence that the variation in age per decade of local density augments, up to a factor of two, for galaxies residing in massive relative to poor groups. (abridged)
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