2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/104780We describe the exponent of a group-theoretical fusion category $\mathcal C = \mathcal C(G, ω, F, α)$ associated to a finite group $G$ in terms of group cohomology. We show that the exponent of $\C$ divides both $e(ω) \exp G$ and $(\exp G)^2$, where $e(ω)$ is the cohomological order of the 3-cocycle $ω$. In particular $\exp \C$ divides $(\dim \C)^2$.22 pages, amslatexQuantum Algebra16W30text