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d6h - Point Group Symmetry Character Tables

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

E2C62C3C23C'23C'2i2S32S6σhdvLinear,
rotations
Quadratic
A1g111111111111x2+y2, z2
A2g1111-1-11111-1-1Rz
B1g1-11-11-11-11-11-1
B2g1-11-1-111-11-1-11
E1g21-1-20021-1-200(Rx, Ry)(xz, yz)
E2g2-1-12002-1-1200(x2-y2, xy)
A1u111111-1-1-1-1-1-1
A2u1111-1-1-1-1-1-111z
B1u1-11-11-1-11-11-11
B2u1-11-1-11-11-111-1
E1u21-1-200-2-11200(x, y)
E2u2-1-1200-211-200

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

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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