We report on the investigation of $Delta$(1232) production and decay in proton-proton collisions at a kinetic energy of 1.25 GeV measured with HADES. Exclusive dilepton decay channels $ppe^{+}e^{-}$ and $ppe^{+}e^{-}gamma$ have been studied and compared with the partial wave analysis of the hadronic $pppi^{0}$ channel. They allow to access both $Delta^+ to ppi^0(e^+e^-gamma)$ and $Delta^+ to pe^+e^-$ Dalitz decay channels. The perfect reconstruction of the well known $pi^0$ Dalitz decay serves as a proof of the consistency of the analysis. The $Delta$ Dalitz decay is identified for the first time and the sensitivity to N-$Delta$ transition form factors is tested. The $Delta$(1232) Dalitz decay branching ratio is also determined for the first time; our result is (4.19 $pm$ 0.62 syst. $pm$ 0.34 stat.) $times $ 10$^{-5}$, albeit with some model dependence.
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