Abstract: Let G be a locally compact group and H be a compact subgroup of G. In this note, we characterize the spectrum of the Banach algebra L1(G/H). Then, by using this result, we show that L1(G/H) is right character amenable if and only if G/H is amenable and also, it is left character amenable if and only if H is normal in G and G/H is amenable.
