We present a detailed study on the magnetic order in the undoped mother compound LaFeAsO of the recently discovered Fe-based superconductor LaFeAsO1-xFx. In particular, we present local probe measurements of the magnetic properties of LaFeAsO by means of 57Fe Mössbauer spectroscopy and muon-spin relaxation in zero external field along with magnetization and resistivity studies. These experiments prove a commensurate static magnetic order with a strongly reduced ordered moment of 0.25(5)muB at the iron site below T(N)=138 K, well separated from a structural phase transition at T(S)=156 K. The temperature dependence of the sublattice magnetization is determined and compared to theory. Using a four-band spin density wave model both, the size of the order parameter and the quick saturation below T(N) are reproduced.