We present a detailed study on the magnetic order in the undoped mother compound LaOFeAs of the recently discovered Fe-based superconductor LaO$_{1-x}$F$_x$FeAs. In particular, we present local probe measurements of the magnetic properties of LaOFeAs by means of $^{57}$Fe Mossbauer 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) $mu_B$ at the iron site below T_N = 138 K, well separated from a structural phase transition at T_N = 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.
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