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D6H - 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

D6h Point Group

not Abelian, 12(16) irreducible representations
Subgroups of D6h point group: Cs, Ci, C2, C3, C6, D2, D3, D6, C2v, C3v, C6v, C2h, C3h, C6h, D2h, D3h, D3d, S6

Character table for D6h point group
E 2C6 2C3 C2 3C'2 3C''2 i 2S3 2S6 σh d v Linear,
rotations
Quadratic
A1g 1 1 1 1 1 1 1 1 1 1 1 1 x2+y2, z2
A2g 1 1 1 1 -1 -1 1 1 1 1 -1 -1 Rz
B1g 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1
B2g 1 -1 1 -1 -1 1 1 -1 1 -1 -1 1
E1g 2 1 -1 -2 0 0 2 1 -1 -2 0 0 (Rx, Ry) (xz, yz)
E2g 2 -1 -1 2 0 0 2 -1 -1 2 0 0 (x2-y2, xy)
A1u 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1
A2u 1 1 1 1 -1 -1 -1 -1 -1 -1 1 1 z
B1u 1 -1 1 -1 1 -1 -1 1 -1 1 -1 1
B2u 1 -1 1 -1 -1 1 -1 1 -1 1 1 -1
E1u 2 1 -1 -2 0 0 -2 -1 1 2 0 0 (x, y)
E2u 2 -1 -1 2 0 0 -2 1 1 -2 0 0

Product table for D6h point group
 A1gA2gB1gB2gE1gE2gA1uA2uB1uB2uE1uE2u
A1gA1gA2gB1gB2gE1gE2gA1uA2uB1uB2uE1uE2u
A2gA2gA1gB2gB1gE1gE2gA2uA1uB2uB1uE1uE2u
B1gB1gB2gA1gA2gE2gE1gB1uB2uA1uA2uE2uE1u
B2gB2gB1gA2gA1gE2gE1gB2uB1uA2uA1uE2uE1u
E1gE1gE1gE2gE2gA1g+A2g+E2gB1g+B2g+E1gE1uE1uE2uE2uA1u+A2u+E2uB1u+B2u+E1u
E2gE2gE2gE1gE1gB1g+B2g+E1gA1g+A2g+E2gE2uE2uE1uE1uB1u+B2u+E1uA1u+A2u+E2u
A1uA1uA2uB1uB2uE1uE2uA1gA2gB1gB2gE1gE2g
A2uA2uA1uB2uB1uE1uE2uA2gA1gB2gB1gE1gE2g
B1uB1uB2uA1uA2uE2uE1uB1gB2gA1gA2gE2gE1g
B2uB2uB1uA2uA1uE2uE1uB2gB1gA2gA1gE2gE1g
E1uE1uE1uE2uE2uA1u+A2u+E2uB1u+B2u+E1uE1gE1gE2gE2gA1g+A2g+E2gB1g+B2g+E1g
E2uE2uE2uE1uE1uB1u+B2u+E1uA1u+A2u+E2uE2gE2gE1gE1gB1g+B2g+E1gA1g+A2g+E2g

Printable D6h point group
Printable character table for D6h point group
Printable product table for D6h point group

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