The structure of magnetic translation group for a finite system

The symmetry group (magnetic translation group) of a Bloch electron in a finite two-dimensional lattice in a perpendicular magnetic field is discussed. The details of the structure of this group depend on a gauge of a vector potential of a magnetic field. For two gauges, symmetric and Landau, the group elements are presented in terms of generators, and the relation between the group properties and the number of magnetic fluxes through the elementary cell of the lattice is pointed out.