We develop methods of computation of the Brauer-Picard groups of fusion
categories and apply them to compute such groups for several classes of fusion
categories of prime power dimension: representation categories of elementary
abelian groups with twisted associativity constraint, extra special p-groups,
and the Kac-Paljutkin Hopf algebra. We conclude that many finite groups of Lie
type occur as composition factors of the Brauer-Picard groups of pointed fusion
categories.
