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Character table for D∞h point group

E 2C ... ∞σv i 2S ... ∞C'2 linear functions,
rotations
quadratic
A1g+g 1 1 ... 1 1 1 ... 1 x2+y2, z2
A2g-g 1 1 ... -1 1 1 ... -1 Rz
E1gg 2 2cos(φ) ... 0 2 -2cos(φ) ... 0 (Rx, Ry) (xz, yz)
E2gg 2 2cos(2φ) ... 0 2 2cos(2φ) ... 0 (x2-y2, xy)
E3gg 2 2cos(3φ) ... 0 2 -2cos(3φ) ... 0
... ... ... ... ... ... ... ... ...
A1u+u 1 1 ... 1 -1 -1 ... -1 z
A2u-u 1 1 ... -1 -1 -1 ... 1
E1uu 2 2cos(φ) ... 0 -2 2cos(φ) ... 0 (x, y)
E2uu 2 2cos(2φ) ... 0 -2 -2cos(2φ) ... 0
E3uu 2 2cos(3φ) ... 0 -2 2cos(3φ) ... 0
... ... ... ... ... ... ... ... ...

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