A type Ia supernova is thought to be a thermonuclear explosion of either a single carbon-oxygen white dwarf or a pair of merging white dwarfs. The explosion fuses a large amount of radioactive Ni-56 (refs 1-3). After the explosion, the decay chain from Ni-56 to Co-56 to Fe-56 generates gamma-ray photons, which are reprocessed in the expanding ejecta and give rise to powerful optical emission. Here we report the detection of Co-56 lines at energies of 847 and 1,238 kiloelectronvolts and a gamma-ray continuum in the 200-400 kiloelectronvolt band from the type Ia supernova 2014J in the nearby galaxy M82. The line fluxes suggest that about 0.6 +/- 0.1 solar masses of radioactive Ni-56 were synthesized during the explosion. The line broadening gives a characteristic mass-weighted ejecta expansion velocity of 10,000 +/- 3,000 kilometres per second. The observed gamma-ray properties are in broad agreement with the canonical model of an explosion of a white dwarf just massive enough to be unstable to gravitational collapse, but do not exclude merger scenarios that fuse comparable amounts of Ni-56.