  (abridged) 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 ~ 1 Mpc, the estimated virial radius of the system. We determine
a total mass of 6x10^{13} M_sun 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 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 ~ 2 keV and a soft X-ray luminosity of
L_x ~ 3 10^{43} erg/s.
