  We discuss the entanglement properties of symmetric states of $n$ qubits. The
Majorana representation maps a generic such state into a system of $n$ points
on a sphere. Entanglement invariants, either under local unitaries (LU) or
stochastic local operations and classical communication (SLOCC), can then be
addressed in terms of the relative positions of the Majorana points. In the LU
case, an over complete set of invariants can be built from the inner product of
the radial vectors pointing to these points; this is detailed for the well
documented three-qubits case. In the SLOCC case, cross ratio of related M^bius
transformations are shown to play a central role, examplified here for four
qubits. Finally, as a side result, we also analyze the manifold of maximally
entangled 3 qubit state, both in the symmetric and generic case.
