If the diphoton excess at 750 GeV hinted by the 2015 data at the LHC is explained in terms of a scalar resonance participating in the breaking of the electroweak symmetry, this resonance must be accompanied by other scalar states for perturbative unitarity in vector-boson scattering to be preserved. The simplest setup consistent with perturbative unitarity and with the data of the diphoton excess is the Georgi-Machacek model. The custodial singlet of the model is responsible for the diphoton excess; it is mainly produced in the diphoton fusion channel, and its loop-induced coupling to the photon pairs is enhanced by the doubly charged scalar with its large (dimensionful) coupling to the custodial singlet.