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The β+/EC decay of 72Kr has been studied by means of the Total Absorption gamma Spectroscopy technique in order to determine the Gamow-Teller strength B(GT) distribution. The comparison with theoretical predictions suggests a dominantly oblate deformation for the 72Kr ground state. The de-excitation of low-energy excited states in 72Br is studied via conversion electron spectroscopy. The conversion coefficients and multipolarities of 14 low-energy transitions are determined and the spin and parity of the levels involved are deduced.