EXTENSIONS OF A NEAR-GROUP CATEGORY OF TYPE (Z2, 1)

We study the G-extensions C of a near-group fusion category of type (Z(2), 1). If C is braided we prove that C can be reconstructed from pointed fusion categories by Z(2)-extensions or Z(2)-equivariantizations. Furthermore, if C is also integral, or C is equivalent as a tensor category to the category of finite dimensional representations of a semisimple Hopf algebra, we prove that C is group-theoretical, which completes the classification of these categories in the sense of Morita equivalence.