Using calculated tables of the second-rank constitutive tensors for linear bianisotropic media, some general electromagnetic properties of the media are discussed. We consider enantiomorphism, crosscoupling tensors and nonreciprocity. The presented tables obtained by group-theoretical methods and comprising 122 discrete point and 21 continuous magnetic groups of symmetry can serve for investigation of some other physical properties of the media. Also considered are the main distinctions of the tables from those published earlier.