  RhGe synthesized at high pressure is crystallized in noncentrosymmetric cubic
structure of the B20 type. Measurements of the electrical resistivity and
magnetization demonstrate a superconducting state below T$_c$ ~ 4.5 K and a
weak ferromagnetism below T$_m$ ~ 140 K. Specific heat data confirm the bulk
nature of superconductivity in this ferromagnetic superconductor. The
superconducting region forms a dome on the P-T diagram with a maximum of T$_c$
near 4 GPa. Ab initio simulations suggest that the observed weak magnetization
emerges from the pronounced spin polarization with magnetic quadrupole and
toroidal moments located at Rh and Ge sites.
