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In this paper we present the first study of the impact of the$\mathcal{O}(\alpha)$ EW correction to the $pp \to ZZ \gamma+X$ process at theCERN Large Hadron Collider (LHC). The subsequent $Z$-boson leptonic decays areconsidered at the leading order using the MadSpin method, which takes intoaccount the spin-correlation and off-shell effects from the $Z$-boson decays.We provide numerical results of the integrated cross section and the kinematicdistributions for this process. In coping with final-state photon-jetseparation in the QCD real emission and photon-induced processes, we adopt boththe Frixione isolated-photon plus jets algorithm and the phenomenologicalquark-to-photon fragmentation function method for comparison. We find that thenext-to-leading order (NLO) EW correction to the $ZZ\gamma$ production can besizeable and amounts to about $-7\%$ of the integrated cross section, andprovides a non$-$negligible contribution to the kinematic distributions,particularly in the high energy region. We conclude that the NLO EW correctionshould be included in precision theoretical predictions in order to matchfuture experimental accuracy.

$ZZ\gamma$ production in the NLO QCD+EW accuracy at the LHC