Strength of the upper brittle part of the Earth's lithosphere controls deformation styles in tectonically active regions, surface topography, seismicity, and the occurrence of plate tectonics, yet it remains one of the least constrained and most debated quantities in geophysics. Seismic data (in particular, earthquake focal mechanisms) have been used to infer orientation of the principal stress axes. Here I show that the focal mechanism data can be combined with information from precise earthquake locations to place robust constraints not only on the orientation, but also on the magnitude of absolute stress at depth. The proposed method uses machine learning to identify quasi-linear clusters of seismicity associated with active faults. A distribution of the relative attitudes of conjugate faults carries information about the amplitude and spatial heterogeneity of the deviatoric stress and frictional strength in the seismogenic zone. The observed diversity of dihedral angles between conjugate faults in the Ridgecrest (California, USA) area that hosted a recent sequence of strong earthquakes suggests the effective coefficient of friction of 0.4-0.6, and depth-averaged shear stresses on the order of 25-40 MPa, intermediate between predictions of the "strong" and "weak" fault theories.