Monoisotopic samples of exotic, neutron-rich 117 Rh nuclei, produced in the proton-induced fission of 238 U and separated using the IGISOL mass separator coupled to the JYFLTRAP Penning trap, were used to perform β and γ coincidence spectroscopy of 117 Pd. The spin parity of the ground state of 117 Pd was determined to be 1/2 + and the 19.1 ms isomer at 203.2 keV was assigned a spin-parity 7/2 − . The 117 Rh β − -decay scheme was considerably extended, and various sequences of the levels were interpreted as resulting from the prolate, oblate, and triaxial nuclear shapes. Some of the β − decays were considered as the allowed Gamow-Teller transitions. The experimental distribution of Gamow-Teller strength is discussed.