A silencer for an auxiliary power unit of an aircraft includes an inlet, an outlet, a housing, and a flow channel of a porous material, arranged in the housing. Between the housing and the flow channel an intermediate space is created, which space is divided by at least one outer partition into outer cells arranged around the flow channel. A central body includes a casing that is permeable to gas at least in some regions and that is arranged in the interior of the silencer. The central body includes inner partitions dividing the central body into inner cells. The resonance frequency of the inner cells corresponds to the natural frequency of the first radial mode in a channel formed between the central body and the inner surface of the inlet. In this manner particularly good sound attenuation is achieved with a compact installation space of a silencer.