************************************************************************* 71149 We propose to observe the nearby group of galaxy NGC5044 group, to perform hard X-ray deep imaging of non-thermal hard X-ray. This non- thermal X-ray implies very important issues: particle acceleration and non-thermal pressure in clusters. The emission mechanism is thought to be inverse Compton scattering of CMB by relastivitic electrons or non- thermal bremsstrahlung between hot plasma and sub-relativistic particles. The distribution and spectral change of non-thermal hard X- ray is expected to constrain the emission mechanism. *************************************************************************