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d4h - Point Group Symmetry Character Tables


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

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
E 2C4 (z) C2 2C'2 2C''2 i 2S4 σh v d linears,
rotations
quadratic
A1g 1 1 1 1 1 1 1 1 1 1 x2+y2, z2
A2g 1 1 1 -1 -1 1 1 1 -1 -1 Rz
B1g 1 -1 1 1 -1 1 -1 1 1 -1 x2-y2
B2g 1 -1 1 -1 1 1 -1 1 -1 1 xy
Eg 2 0 -2 0 0 2 0 -2 0 0 (Rx, Ry) (xz, yz)
A1u 1 1 1 1 1 -1 -1 -1 -1 -1
A2u 1 1 1 -1 -1 -1 -1 -1 1 1 z
B1u 1 -1 1 1 -1 -1 1 -1 -1 1
B2u 1 -1 1 -1 1 -1 1 -1 1 -1
Eu 2 0 -2 0 0 -2 0 2 0 0 (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

Printable D4h point group
Printable character table for D4h point group
Printable product table for D4h point group

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