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OH - 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

Oh Point Group

not Abelian, 10(20) irreducible representations

Character table for Oh point group
E 8C3 6C2 6C4 3C2 =(C4)2 i 6S4 8S6 h d linear,
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
Eg 2 -1 0 0 2 2 0 -1 2 0 (2z2-x2-y2, x2-y2)
T1g 3 0 -1 1 -1 3 1 0 -1 -1 (Rx, Ry, Rz)
T2g 3 0 1 -1 -1 3 -1 0 -1 1 (xz, yz, xy)
A1u 1 1 1 1 1 -1 -1 -1 -1 -1
A2u 1 1 -1 -1 1 -1 1 -1 -1 1
Eu 2 -1 0 0 2 -2 0 1 -2 0
T1u 3 0 -1 1 -1 -3 -1 0 1 1 (x, y, z)
T2u 3 0 1 -1 -1 -3 1 0 1 -1

Product table for Oh point group
 A1gA2gEgT1gT2gA1uA2uEuT1uT2u
A1gA1gA2gEgT1gT2gA1uA2uEuT1uT2u
A2gA2gA1gEgT2gT1gA2uA1uEuT2uT1u
EgEgEgA1g+A2g+EgT1g+T2gT1g+T2gEuEuA1u+A2u+EuT1u+T2uT1u+T2u
T1gT1gT2gT1g+T2gA1g+Eg+T1g+T2gA2g+Eg+T1g+T2gT1uT2uT1u+T2uA1u+Eu+T1u+T2uA2u+Eu+T1u+T2u
T2gT2gT1gT1g+T2gA2g+Eg+T1g+T2gA1g+Eg+T1g+T2gT2uT1uT1u+T2uA2u+Eu+T1u+T2uA1u+Eu+T1u+T2u
A1uA1uA2uEuT1uT2uA1gA2gEgT1gT2g
A2uA2uA1uEuT2uT1uA2gA1gEgT2gT1g
EuEuEuA1u+A2u+EuT1u+T2uT1u+T2uEgEgA1g+A2g+EgT1g+T2gT1g+T2g
T1uT1uT2uT1u+T2uA1u+Eu+T1u+T2uA2u+Eu+T1u+T2uT1gT2gT1g+T2gA1g+Eg+T1g+T2gA2g+Eg+T1g+T2g
T2uT2uT1uT1u+T2uA2u+Eu+T1u+T2uA1u+Eu+T1u+T2uT2gT1gT1g+T2gA2g+Eg+T1g+T2gA1g+Eg+T1g+T2g

Printable Oh point group
Printable character table for Oh point group
Printable product table for Oh point group

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