  Bloch oscillations originate from the translational symmetry of crystals.
These oscillations occur with a fundamental period that a semiclassical
wavepacket takes to traverse a Brillouin-zone loop. We introduce a new type of
Bloch oscillations whose periodicity is an integer ($\mu{>}1$) multiple of the
fundamental period. The period multiplier $\mu$ is a topological invariant
protected by the space groups of crystals, which include more than just
translational symmetries. For example, $\mu$ divides $n$ for crystals with an
$n$-fold rotational or screw symmetry; with a reflection, inversion or glide
symmetry, $\mu$ equals two. We identify the commonality underlying all
period-multiplied oscillations: the multi-band Berry-Zak phases, which encode
the holonomy of adiabatic transport of Bloch functions in quasimomentum space,
differ pairwise by integer multiples of $2\pi/\mu$. For a class of multi-band
subspaces whose projected-position operators commute, period multiplication has
a complementary explanation through the real space distribution of Wannier
functions. This complementarity follows from a one-to-one correspondence
between Berry-Zak phases and the centers of Wannier functions. A Wannier
description of period multiplication does not always exist, as we exemplify
with band subspaces with either a nonzero Chern number or $\mathbb{Z}_2$
Kane-Mele topological order. To help identify band subspaces with $\mu{>}1$, a
general theorem is presented that outputs Zak phases that are
symmetry-protected to integer multiples of $2\pi/n$, given the point-group
symmetry representation of any gapped band subspace. A cold-atomic experiment
that has observed period-multiplied Bloch oscillations is discussed, and
directions are provided for future experiments.
