InverseAfterComplementAfterReverse from Permutation
Reverse, then complement, then invert.
The name is FindStat's, and it is what a catalog produces when it cannot SAY composition. With Composition it is Compose(Inverse, Complement, Reverse) and needs no name at all — kept only because the catalog has it.
Called as CombinatorialMap(x, "InverseAfterComplementAfterReverse"). The head's page has its examples.