  We develop the symmetry classification of superconducting gap functions in
electron bands that do not transform under the crystal point group operations
like the pure spin-1/2 states. The Bloch state bases in twofold degenerate
bands with spin-orbit coupling are defined across the Brillouin zone in the way
which satisfies the symmetry and continuity requirements. These bases are used
to construct general multiband pairing Hamiltonians in centrosymmetric
crystals. Focusing on single-band pairing, four exceptional cases are
identified in which the triplet gap function does not transform under the point
group operations as a pseudovector, with a significant impact on the nodal
structure.
