Controlling the flow of quantum information is a fundamental task for quantum computers, which is unfeasible to realize on classical devices. Coherent devices, which can process quantum states are thus required to route the quantum states that encode information. In this paper we demonstrate experimentally the smallest quantum transistor with a superconducting quantum processor, which is composed of a collector qubit, an emitter qubit, and a coupler (transistor gate). The interaction strength between the collector and emitter qubits is controlled by the frequency and state of the coupler, effectively implementing a quantum switch. Through the coupler-state-dependent Heisenberg (inherent) interaction between the qubits, a single-step (native) conditional iSWAP operation can be applied. To this end, we find that it is useful to take into consideration the higher-energy level for achieving a native and high-fidelity transistor operation. By reconstructing the quantum process tomography, we obtain an operation fidelity of 92.36% when the transistor gate is open (iSWAP implementation) and 95.23% in the case of closed gate (identity gate implementation). The architecture has strong potential in quantum information processing applications with superconducting qubits.