Galilei relativity principle in classical electrodynamics

A theorem is formulated that Galilei group is that of Maxwell equation exact symmetry group, providing the fields are transformed by nonlinear representation of this group. Galilei symmetry differs from the relativistic one in the fact that relativistic symmetry is manifested while postulating the light velocity invariance, whereas Galilei symmetry is manifested during postulating time invariance. In relativistic case the field transformations are linear and global, in Galilei case they are nonlinear and evidently depend on time and coordinates. Existence of Galilei symmetry for Maxwell equations means that in a certain sense, Galilei relativity principle holds not only in classical mechanics but in classical electrodynamics too