We report on the spin and occupation noise of a single, positively charged (InGa)As quantum dot emitting photons in the telecommunication C-band. The spin noise spectroscopy measurements are carried out at a temperature of 4.2 K in dependence on intensity and detuning in the regime beyond thermal equilibrium. The spin noise spectra yield in combination with an elaborate theoretical model the hole-spin relaxation time of the positively charged quantum dot and the Auger recombination and the electron-spin relaxation time of the trion state. The extracted Auger recombination time of this quantum dot emitting at 1.55 μm is comparable to the typical Auger recombination times on the order of a few μs measured in traditionally grown InAs/GaAs quantum dots emitting at around 900 nm.