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d_h - Point Group Symmetry Character Tables

D∞h Point Group

not Abelian, ∞ irreducible representations

Character table for D∞h point group

E2C...∞σvi2S...∞C'2linear functions,
rotations
quadratic
A1g+g11...111...1x2+y2, z2
A2g-g11...-111...-1Rz
E1gg22cos(φ)...02-2cos(φ)...0(Rx, Ry)(xz, yz)
E2gg22cos(2φ)...022cos(2φ)...0(x2-y2, xy)
E3gg22cos(3φ)...02-2cos(3φ)...0
...........................
A1u+u11...1-1-1...-1z
A2u-u11...-1-1-1...1
E1uu22cos(φ)...0-22cos(φ)...0(x, y)
E2uu22cos(2φ)...0-2-2cos(2φ)...0
E3uu22cos(3φ)...0-22cos(3φ)...0
...........................


C1 Cs Ci
C2 C3 C4 C5 C6
C2v C3v C4v C5v C6v
C2h C3h C4h C5h C6h
D2 D3 D4 D5 D6
D2h D3h D4h D5h D6h
D2d D3d D4d D5d D6d
S4 S6 S8 S10
Td Oh Ih
C∞v D∞h

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