  We summarize basic features of quantum field theories with discrete symmetry
$\mathbb{Q}/\mathbb{Z}$ (possibly higher form, global or gauged). The
classification of representations and anomalies is quite rich and involves the
ring of profinite integers. As a main example we consider in detail 3d
topological Dijkgraaf-Witten $\mathbb{Q}/\mathbb{Z}$ gauge theories. We also
briefly discuss relevance for some previously considered physical systems. In
particular we comment on a relation to the recently discovered non-invertible
symmetry in 4d QED and the problem of categorification of Chern-Simons TQFT.
