A β-decaying high-spin isomer in (96)Cd, with a half-life T(1/2)=0.29(-0.10)(+0.11) s, has been established in a stopped beam rare isotope spectroscopic investigations at GSI (RISING) experiment. The nuclei were produced using the fragmentation of a primary beam of (124)Xe on a (9)Be target. From the half-life and the observed γ decays in the daughter nucleus, (96)Ag, we conclude that the β-decaying state is the long predicted 16(+) "spin-gap" isomer. Shell-model calculations, using the Gross-Frenkel interaction and the πν(p(1/2),g(9/2)) model space, show that the isoscalar component of the neutron-proton interaction is essential to explain the origin of the isomer. Core excitations across the N=Z=50 gaps and the Gamow-Teller strength, B(GT) distributions have been studied via large-scale shell-model calculations using the πν(g,d,s) model space to compare with the experimental B(GT) value obtained from the half-life of the isomer.