The shell structure of atomic nuclei is associated with ‘magic numbers’ and originates in the nearly independent motion of neutrons and protons in a mean potential generated by all nucleons. During β+-decay, a proton transforms into a neutron in a previously not fully occupied orbital, emitting a positron–neutrino pair with either parallel or antiparallel spins, in a Gamow–Teller or Fermi transition, respectively. The transition probability, or strength, of a Gamow–Teller transition depends sensitively on the underlying shell structure and is usually distributed among many states in the neighbouring nucleus. Here we report measurements of the half-life and decay energy for the decay of 100Sn, the heaviest doubly magic nucleus with equal numbers of protons and neutrons. In the β-decay of 100Sn, a large fraction of the strength is observable because of the large decay energy. We determine the largest Gamow–Teller strength so far measured in allowed nuclear β-decay, establishing the ‘superallowed’ nature of this Gamow–Teller transition. The large strength and the low-energy states in the daughter nucleus, 100In, are well reproduced by modern, large-scale shell model calculations.