  We present the results of the analysis of the ROSAT PSPC pointed observation
of the S0 galaxy NGC5866. Previous Einstein observations had revealed that this
galaxy has a low X-ray to optical ratio Lx/Lb. Theoretical models of the X-ra
emission of early-type galaxies had suggested that in objects of this kind the
emission is not dominated by the presence of a hot diffuse gas, but should
originate in stellar sources. We discuss the evidence in favor of this
hypothesis following from the results of the analysis of the ROSAT PSPC data.
The X-ray spectrum shows properties similar to those of the other two low Lx/Lb
early-type galaxies observed by ROSAT so far, including the presence of very
soft emission. So, these galaxies can be recognized as a group with homogeneous
properties, and a more exhaustive picture of the nature of the X-ray emission
across the Lx/Lb plane of early-type galaxies can be outlined. We also discuss
the importance of rotation in the X-ray emission of S0 galaxies, and suggest
that it could explain why on average S0s are less X-ray luminous than
ellipticals.
