`Galaxy groups' have hardly been realized as a separate class of objects with specific characteristics in the structural hierarchy of the universe. The presumption that the self-similarity of dark matter structures is a valid prescription for the baryonic universe also at all scales has rendered smaller structures undetectable by current observational facilities, leading to lesser dedicated studies on them. Some recent reports on deviation of $\rm{L_x}$-T scaling in groups from that of clusters have motivated us to study their physical properties in depth. In this article, we report the extensive study on physical properties of groups in comparison with clusters through cosmological hydrodynamic plus N-body simulations using ENZO 2.2 code. We have included cooling and heating physics and star formation feedback in the simulation. And produced a mock sample of 362 objects with mass ranging from $5\times10^{12}\; \rm{M_{\odot}}$ to 2.5$\times 10^{15}\; \rm{M_{\odot}}$. Strikingly, we have found that objects with a mass below $\sim$ $8\times 10^{13}\;\rm{M_{\odot}}$ do not follow any of the cluster self-similar laws in hydrostatics, not even in thermal and non-thermal regimes. Two distinct scaling laws are observed to be followed with breaks at $\sim$ $6-8\times 10^{13}\;\rm{M_{\odot}}$ for mass, $\sim$1 keV for temperature and $\sim$1 Mpc for radius. This places groups as a distinct entity in the hierarchical structures, well demarcated from clusters. This study reveals that groups are mostly far away from virialization, suggesting the need for formulating new models for deciphering their physical parameters. They are also shown to have high turbulence and more non-thermal energy stored, indicating better visibility in the non-thermal regime.

The project is funded by DST INSPIRE Faculty (IFA-12/PH-44) and DST-SERB Fast Track scheme for young scientists, Grant No. SR/FTP/PS-118/2011. We are thankful to the Inter-University Centre for Astronomy and Astrophysics (IUCAA) for providing the HPC facility. RSJ acknowledge with thanks the facilities provided by IUCAA as a visiting student.Computations described in this work were performed using the publicly-available Enzo code (http://enzo-project.org) and data analysis is done with the yt-tools (http://yt-project.org/).