  A one-dimensional quantum charge pump transfers a quantized charge in each
pumping cycle. This quantization is topologically robust being analogous to the
quantum Hall effect. The charge transferred in a fraction of the pumping period
is instead generally unquantized. We show, however, that with specific
symmetries in parameter space the charge transferred at well-defined fractions
of the pumping period is quantized as integer fractions of the Chern number. We
illustrate this in a one-dimensional Harper-Hofstadter model and show that the
fractional quantization of the topological charge pumping is independent of the
specific boundary conditions taken into account. We further discuss the
relevance of this phenomenon for cold atomic gases in optical superlattices.
