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

Character table
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
 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

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