  We classify all groups G and all pairs (V,W) of absolutely simple
Yetter-Drinfeld modules over G such that the support of the direct sum of V and
W generates G, the square of the braiding between V and W is not the identity,
and the Nichols algebra of the direct sum of V and W admits a finite root
system. As a byproduct, we determine the dimensions of such Nichols algebras,
and several new families of finite-dimensional Nichols algebras are obtained.
Our main tool is the Weyl groupoid of pairs of absolutely simple
Yetter-Drinfeld modules over groups.
