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d4h - Point Group Symmetry Character Tables

D4h Point Group

not Abelian, 10(12) irreducible representations
Subgroups of D4h point group: Cs, Ci, C2, C4, D2, D4, C2v, C4v, C2h, C4h, D2h, D2d, S4

Character table for D4h point group

E2C4 (z)C22C'22C''2i2S4σhvdlinears,
rotations
quadratic
A1g1111111111x2+y2, z2
A2g111-1-1111-1-1Rz
B1g1-111-11-111-1x2-y2
B2g1-11-111-11-11xy
Eg20-20020-200(Rx, Ry)(xz, yz)
A1u11111-1-1-1-1-1
A2u111-1-1-1-1-111z
B1u1-111-1-11-1-11
B2u1-11-11-11-11-1
Eu20-200-20200(x, y)

Product table for D4h point group

 A1gA2gB1gB2gEgA1uA2uB1uB2uEu
A1gA1gA2gB1gB2gEgA1uA2uB1uB2uEu
A2gA2gA1gB2gB1gEgA2uA1uB2uB1uEu
B1gB1gB2gA1gA2gEgB1uB2uA1uA2uEu
B2gB2gB1gA2gA1gEgB2uB1uA2uA1uEu
EgEgEgEgEgA1g+A2g+B1g+B2gEuEuEuEuA1u+A2u+B1u+B2u
A1uA1uA2uB1uB2uEuA1gA2gB1gB2gEg
A2uA2uA1uB2uB1uEuA2gA1gB2gB1gEg
B1uB1uB2uA1uA2uEuB1gB2gA1gA2gEg
B2uB2uB1uA2uA1uEuB2gB1gA2gA1gEg
EuEuEuEuEuA1u+A2u+B1u+B2uEgEgEgEgA1g+A2g+B1g+B2g

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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