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Abstract The ALICE Collaboration at the CERN LHC has measured the inclusive production cross section of isolated photons at midrapidity as a function of the photon transverse momentum ($$p_{\textrm{T}}^{\gamma }$$ $p_{\text{T}}^{\gamma }$), in Pb–Pb collisions in different centrality intervals, and in pp collisions, at centre-of-momentum energy per nucleon pair of$$\sqrt{s_{\textrm{NN}}}~=~5.02$$ $\sqrt{s_{\text{NN}}}=5.02$ TeV. The photon transverse momentum range is between 10–14 and 40–140 GeV/$$c$$ $c$, depending on the collision system and on the Pb–Pb centrality class. The result extends to lower$$p_{\textrm{T}}^{\gamma }$$ $p_{\text{T}}^{\gamma }$than previously published results by the ATLAS and CMS experiments at the same collision energy. The covered pseudorapidity range is$$|\eta ^{\gamma } | <0.67$$ $|{\eta }^{\gamma }|<0.67$. The isolation selection is based on a charged particle isolation momentum threshold$$p_{\textrm{T}}^\mathrm{iso,~ch} = 1.5$$ $p_{\text{T}}^{\mathrm{iso},\mathrm{ch}}=1.5$ GeV/$$c$$ $c$within a cone of radii$$R=0.2$$ $R=0.2$and 0.4. The nuclear modification factor is calculated and found to be consistent with unity in all centrality classes, and also consistent with the HG-PYTHIA model, which describes the event selection and geometry biases that affect the centrality determination in peripheral Pb–Pb collisions. The measurement is compared to next-to-leading order perturbative QCD calculations and to the measurements of isolated photons and Z$$^{0}$$ $_{}^0$bosons from the CMS experiment, which are all found to be in agreement.