We present mass and entropy radial profiles for 16 relaxed galaxy groups-poor clusters selected among the brightest in the Chandra and XMM archives. After accounting for the mass of the hot gas, the resulting mass profiles are described well by a two-component model consisting of dark matter represented by an NFW model, and stars form the central galaxy. We find for the first time that the NFW concentration parameter (c_vir) for groups decreases with increasing M_vir. The mean gas fraction of the groups measured within an over-density of 2500 is lower than for hot, massive cluster with a larger fractional scatter implying a greater impact of feedback processes on groups. This is reflected in the entropy profiles which show striking deviations from self-similarity, large object-to-object variation and a characteristic broken-power-law behavior, unlike more massive clusters. We present the interesting cases of two groups: NGC 5044 and AWM4. NGC 5044 shows in the inner 10 kpc a pair of cavities together with a set of bright filaments and two sloshing cold fronts, for the first time revealed in a group of galaxies. AWM 4 is characterized by a combination of properties which seems to defy the paradigm for AGN heating in cluster cores.