  We present an analysis of the properties of the ICM in an extended set of
cosmological hydrodynamical simulations of galaxy clusters and groups performed
with the TreePM+SPH GADGET-3 code. Besides a set of non-radiative simulations,
we carried out two sets of simulations including radiative cooling, star
formation, metal enrichment and feedback from supernovae, one of which also
accounts for the effect of feedback from AGN resulting from gas accretion onto
super-massive black holes. These simulations are analysed with the aim of
studying the relative role played by SN and AGN feedback on the general
properties of the diffuse hot baryons in galaxy clusters and groups: scaling
relations, temperature, entropy and pressure radial profiles, and ICM chemical
enrichment. We find that simulations including AGN feedback produce scaling
relations that are in good agreement with X-ray observations at all mass
scales. However, our simulations are not able to account for the observed
diversity between CC and NCC clusters: unlike for observations, we find that
temperature and entropy profiles of relaxed and unrelaxed clusters are quite
similar and resemble more the observed behaviour of NCC clusters. As for the
pattern of metal enrichment, we find that an enhanced level of iron abundance
is produced by AGN feedback with respect to the case of purely SN feedback. As
a result, while simulations including AGN produce values of iron abundance in
groups in agreement with observations, they over-enrich the ICM in massive
clusters. The efficiency of AGN feedback in displacing enriched gas from halos
into the inter-galactic medium at high redshift also creates a widespread
enrichment in the outskirts of clusters and produces profiles of iron abundance
whose slope is in better agreement with observations.
