We present results from an analysis of the X-ray properties of the NGC 383 galaxy group based on ROSAT PSPC and HRI data . X-ray emission can be traced out to \sim 1 h _ { 50 } ^ { -1 } Mpc , the estimated virial radius of the system . We determine a total mass of 6 10 ^ { 13 } h _ { 50 } ^ { -1 } M _ { \odot } for the group inside this radius with a gas mass fraction of 21 % . The intragroup gas temperature of 1.5 keV is both consistent with the galaxy velocity dispersion and the X-ray luminosity - temperature relation of groups and clusters suggesting that the group is fairly relaxed . This is also indicated by the almost spherically symmetric appearance of the group ’ s X-ray halo . The X-ray properties of the radio galaxy NGC 383 ( 3C 31 ) which is located near the center of the group are discussed . Its spectrum is best described by a two-component model , consisting of emission from a low-temperature Raymond-Smith plasma , and a hard tail . The emission from NGC 383 is not resolved by the ROSAT HRI . The possible interaction of the radio jets of 3C 31 with the IGM is studied . A spatial , spectral and temporal analysis of the Einstein source 1E0104+3153 located within the field of view is performed , one goal being the identification of the optical counterpart ( with both , a high-redshift BAL quasar and a nearby elliptical galaxy , member of a small group , located within the Einstein X-ray error circle ) . We find evidence that the IGM of the small group contributes significantly to the X-ray emission of 1E0104 , which can be described by a Raymond-Smith model of kT \simeq 2 keV and a soft X-ray luminosity of L _ { x } \simeq 3 10 ^ { 43 } erg/s .