The INTEGRAL mission provides a large data set for studying the hard X-ray properties of AGN and allows testing of the unified scheme for AGN. We present analysis of INTEGRAL IBIS/ISGRI, JEM-X, and OMC data for 199 AGN supposedly detected by INTEGRAL above 20 keV. The data analysed here allow a significant spectral extraction on 148 objects and an optical variability study of 57 AGN. The slopes of the hard X-ray spectra of Seyfert 1 and Seyfert~2 galaxies are found to be consistent within the uncertainties, whereas higher cut-off energies and lower luminosities are measured for the more absorbed / type 2 AGN. The intermediate Seyfert 1.5 objects exhibit hard X-ray spectra consistent with those of Seyfert 1. When applying a Compton reflection model, the underlying continua appear the same in Seyfert 1 and 2 with photon index 2, and the reflection strength is about R = 1, when assuming different inclination angles. A significant correlation is found between the hard X-ray and optical luminosity and the mass of the central black hole in the sense that the more luminous objects appear to be more massive. There is also a general trend toward the absorbed sources and type 2 AGN having lower Eddington ratios. The black holemass appears to form a fundamental plane together with the optical and X-ray luminosity of the form Lv being proportional to Lx^0.6 M^0.2, similar to that found between radio luminosity Lr, Lx, and M. The unified model for Seyfert galaxies seems to hold, showing in hard X-rays that the central engine is the same in Seyfert 1 and 2, but seen under different inclination angles and absorption. (Abridged)
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