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The space-group approach to the wavefunction of a Cooper pair is extended toShubnikov groups of type III and applied to newly discovered nearlyferromagnetic superconductor UTe2. A nonunitary triplet SOP (superconductingorder parameter), manifested experimentally, was obtained for Shubnikov groupm'm'm . The nodal structure of triplet nonunitary SOP is investigated and itwas shown that in the case of Shubnikov III symmetry nodal structure of ESP(equal spin pairing) state is in some cases unstable, i.e. changes when acomplex phase winding is added. The irreducible corepresentations of a Cooperpair wave function corresponding to m'm'm symmetry and to all experimental datafor UTe2 are identified.

Time-Reversal Symmetry and the Structure of Superconducting Order Parameter of Nearly Ferromagnetic Spin-Triplet Superconductor UTe2