Let \(\cal{K}\) be the smallest dimensional non-pointed basic Hopf algebra. We determine all finite-dimensional Nichols algebras in \({}^{\cal{K}}_{\cal{K}}\cal{Y}\cal{D}\) and compute the liftings. The result shows that there are some new Nichols algebras of non-diagonal type and new finite-dimensional Hopf algebras without the dual Chevalley property.
