A search for radiative decays of the P-wave spin singlet charmonium resonance h_{c} is performed based on 4.48×10^{8} ψ^{'} events collected with the BESIII detector operating at the BEPCII storage ring. Events of the reaction channels h_{c}→γη^{'} and γη are observed with a statistical significance of 8.4σ and 4.0σ, respectively, for the first time. The branching fractions of h_{c}→γη^{'} and h_{c}→γη are measured to be B(h_{c}→γη^{'})=(1.52±0.27±0.29)×10^{-3} and B(h_{c}→γη)=(4.7±1.5±1.4)×10^{-4}, respectively, where the first errors are statistical and the second are systematic uncertainties.
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