  Let X=G/H be the quotient of a connected reductive algebraic C-group G
defined over the field of complex numbers C by a finite subgroup H. We describe
the topological fundamental group of the homogeneous space X, which is
nonabelian when H is nonabelian. Further, we construct an example of a
homogeneous space X and an automorphism s of C such that the topological
fundamental groups of X and of the conjugate variety sX are not isomorphic.
