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The reaction gamma p -> p pi(0)gamma' has been measured with the Crystal Ball/TAPS detectors using the energy-tagged photon beam at the electron accelerator facility MAMI-B. Energy and angular differential cross-sections for the emitted photon gamma' and angular differential cross-sections for the pi(0) have been determined with high statistics in the energy range of the Delta(+)(1232)-resonance. Cross-sections and the ratio of the cross-section to the nonradiative process gamma p -> p pi(0) are compared to theoretical reaction models, having the anomalous magnetic moment kappa(Delta+) as free parameter. As the shape of the experimental distributions is not reproduced in detail by the model calculations, currently no extraction of kappa(Delta+) is feasible.