Transmission for a vehicle

A transmission for a vehicle, the transmission comprising a first input shaft, a second input shaft and a clutch by which the first input shaft and the second input shaft are selectively connectable to an engine, and an electric machine directly connected to the first input shaft, the transmission further comprising an output shaft connected to a final drive, and a further electric machine directly connected to the second input shaft, wherein the first input shaft is permanently connected to the output shaft and the second input shaft is connectable to the output shaft, and wherein the second input shaft is connectable to the output shaft through a gear wheel arranged on the second input shaft and an idling gear wheel arranged on the output shaft, the gear wheel of the second input shaft and the idling gear wheel of the output shaft being engaged with each other, and the idling gear wheel of the output shaft being rotationally lockable to the output shaft, wherein the electric machine has a rated power exceeding the rated power of the further electric machine such that the electric machine together with the further electric machine are dimensioned for all pure electric drive modes and the further electric machine is sufficient for generating power via the engine when driving at low speeds utilizing torque and limited power.