Categorical Lagrangian Grassmannians and Brauer–Picard groups of pointed fusion categories

We analyze the action of the Brauer–Picard group of a pointed fusion category on the set of Lagrangian subcategories of its center. Using this action we compute the Brauer–Picard groups of pointed fusion categories associated to several classical finite groups. As an application, we construct examples of weakly group-theoretical fusion categories.