Using a statistically representative sample of 911 central galaxies (CENs) from the Sloan Digital Sky Survey (SDSS) Data Release 4 group catalogue, we study how the structure (shape and size) of the first rank (by stellar mass) group and cluster members depends on (1) galaxy stellar mass (M_star_), (2) the global environment defined by the dark matter halo mass (M_halo_) of the host group and (3) the local environment defined by their special halocentric position. We quantify the structure of SDSS galaxies with a galfit-based pipeline that fits two-dimensional Sersic models to the r-band image data. Through tests with simulated and real galaxy images, we demonstrate that our pipeline can recover Sersic parameters without significant bias. Moreover, to test the impact of local environment on CENs, we compare the structure of CENs with that satellite galaxies (SATs) of comparable M_star_.