picard group of dual categories

We provide an explicit description of the picard group (the group of isomorphism classes of invertible objects, those that have an inverse under the tensor product) of the dual category of the category of comodules over a supergroup algebra, by using the description of this group for group-theoretical categories. in fact we prove that there is a subgroup relation between these groups. as an interest application of this group in a modular context, it can be used to construct examples of symmetric special frobenius algebras.  they also plays an important role in the theory of braided tensorcategories for the classification of group extensions of fusion categories.