  In [Science 340:1205, (2013)], via entanglement polytopes Michael Walter et
al. obtained a finite yet systematic classification of multi-particle
entanglement. It is well known that under SLOCC, pure states of three (four)
qubits are partitioned into six (nine) families. In this paper,we present a LU
invariant and an entanglement measures for the GHZ SLOCC class of three qubits,
and partition states of the GHZ SLOCC class of three qubits into ten families
and each family into two subfamilies under LU. We give a necessary and
sufficient condition for the uniqueness of the generalized Schmidt
decomposition for the GHZ SLOCC class.
