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In [Science 340:1205, (2013)], via entanglement polytopes Michael Walter etal. obtained a finite yet systematic classification of multi-particleentanglement. 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 LUinvariant 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 familiesand each family into two subfamilies under LU. We give a necessary andsufficient condition for the uniqueness of the generalized Schmidtdecomposition for the GHZ SLOCC class.

Partition GHZ SLOCC class of three qubits into ten families under LU