  `Galaxy groups' have hardly been realised as a separate class of objects with
specific characteristics in the structural hierarchy. The presumption that the
self-similarity of dark matter structures is a valid prescription for the
baryonic universe at all scales has rendered smaller structures undetectable by
current observational facilities, leading to lesser dedicated studies on them.
Some recent reports that indicate a deviation from $\rm{L_x}$-T scaling in
groups compared to 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 to the clusters through cosmological
hydrodynamic plus N-body simulations using ENZO 2.2 code. As additional
physics, radiative cooling, heating due to supernova and star motions, star
formation and stellar feedback has been implemented. We have 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 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 energies. Two distinct scaling laws are observed to be followed
with breaks at $\sim$ $8\times 10^{13}\;\rm{M_{\odot}}$ 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.
