The relation between the factor systems of a group and the factor systems of an invariant subgroup is discussed both for PU and for PUA representations. The results are used to discuss the factor systems of a class of magnetic space groups.
van den Broek, P. M. (1976). The relation between the factor systems of a group and those of an invariant subgroup. Journal of physics A: mathematical and general, 9(6), 855-862. [10.1088/0305-4470/9/6/007]. https://doi.org/10.1088/0305-4470/9/6/007