Computing the Group of Minimal Non-degenerate Extensions of a Super-Tannakian Category

We prove an analog of the Künneth formula for the groups of minimal non-degenerate extensions (Lan et al. in Commun Math Phys 351:709–739, 2017) of symmetric fusion categories. We describe in detail the structure of the group of minimal extensions of a pointed super-Tannakian fusion category. This description resembles that of the third cohomology group of a finite abelian group. We explicitly compute this group in several concrete examples.