New large-rank Nichols algebras over nonabelian groups with commutator subgroup Z2

Our construction uses the new notion of a covering Nichols algebra as a special case of a covering Hopf algebra [18] and produces non-faithful Nichols algebras. We give faithful examples of Doi twists for type A3,C3,D4,C4,F4 over several nonabelian groups of order 16 and 32. These are hence the first known examples of nondiagonal, finite-dimensional, indecomposable Nichols algebras of rank >2 over nonabelian groups.