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D2h point group
Abelian, 8 irreducible representations
Subgroups: Cs, Ci, C2, C2v, C2h

Character table
E C2 (z) C2 (y) C2 (x) i σ (xy) σ (xz) σ (yz)
linear,
rotations
quadratic
Ag 1 1 1 1 1 1 1 1 x2, y2, z2
B1g 1 1 -1 -1 1 1 -1 -1 Rz xy
B2g 1 -1 1 -1 1 -1 1 -1 Ry xz
B3g 1 -1 -1 1 1 -1 -1 1 Rx yz
Au 1 1 1 1 -1 -1 -1 -1
B1u 1 1 -1 -1 -1 -1 1 1 z
B2u 1 -1 1 -1 -1 1 -1 1 y
B3u 1 -1 -1 1 -1 1 1 -1 x

Product table
 AgB1gB2gB3gAuB1uB2uB3u
AgAgB1gB2gB3gAuB1uB2uB3u
B1gB1gAgB3gB2gB1uAuB3uB2u
B2gB2gB3gAgB1gB2uB3uAuB1u
B3gB3gB2gB1gAgB3uB2uB1uAu
AuAuB1uB2uB3uAgB1gB2gB3g
B1uB1uAuB3uB2uB1gAgB3gB2g
B2uB2uB3uAuB1uB2gB3gAgB1g
B3uB3uB2uB1uAuB3gB2gB1gAg

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