  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
$pp\pi^{0}$ channel. They allow to access both $\Delta^+ \to
p\pi^0(e^+e^-\gamma)$ 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.
