  We present the Feedback Acting on Baryons in Large-scale Environments (FABLE)
suite of cosmological hydrodynamical simulations of galaxies, groups and
clusters. The simulations use the AREPO moving-mesh code with a set of physical
models for galaxy formation based on the successful Illustris simulation, but
with updated AGN and supernovae feedback models. This allows us to
simultaneously reproduce the observed redshift evolution of the galaxy stellar
mass function together with the stellar and gas mass fractions of local groups
and clusters across a wide range of halo masses. Focusing on the properties of
groups and clusters, we find very good agreement with a range of observed
scaling relations, including the X-ray luminosity--total mass and gas mass
relations as well as the total mass--temperature and Sunyaev-Zel'dovich
flux--mass relations. Careful comparison of our results with scaling relations
based on X-ray hydrostatic masses as opposed to weak lensing-derived masses
reveals some discrepancies, which hint towards a non-negligible X-ray mass bias
in observed samples. We further show that radial profiles of density, pressure
and temperature of the simulated intracluster medium are in very good agreement
with observations, in particular for $r > 0.3\ r_{500}$. In the innermost
regions however we find too large entropy cores, which indicates that a more
sophisticated modelling of the physics of AGN feedback may be required to
accurately reproduce the observed populations of cool-core and non-cool-core
clusters.
