The physical irreducible representations of the magnetic translation group (M.T.G.) defined previously have been found. From these a set of solutions of Schr\"odinger's equation for a Bloch electron in a magnetic field has been constructed. In general the M.T.G. is non-Abelian. However, when the magnetic flux through areas enclosed by any vectors of the Bravais lattice become multiples of an elementary "fluxon" hc/e, the M.T.G. becomes isomorphic to the usual translation group.
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J. Żak (1964) studied this question.
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