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
더 높은
Td
Oh
Ih
선형
C∞v
D∞h

## Ih 점군

비가환군, 10(32) 기약 표현

Ih 점군에 대한 지표표
E 12C5 12(C5)2 20C3 15C2 i 12S10 12(S10)3 20S6 15σ linear,
rotations
Ag 1 1 1 1 1 1 1 1 1 1 x2+y2+z2
T1g 3 -2cos(4π/5) -2cos(2π/5) 0 -1 3 -2cos(2π/5) -2cos(4π/5) 0 -1 (Rx, Ry, Rz)
T2g 3 -2cos(2π/5) -2cos(4π/5) 0 -1 3 -2cos(4π/5) -2cos(2π/5) 0 -1
Gg 4 -1 -1 1 0 4 -1 -1 1 0
Hg 5 0 0 -1 1 5 0 0 -1 1 [2z2-x2-y2, x2-y2, xy, xz, yz]
Au 1 1 1 1 1 -1 -1 -1 -1 -1
T1u 3 -2cos(4π/5) -2cos(2π/5) 0 -1 -3 2cos(2π/5) 2cos(4π/5) 0 1 (x, y, z)
T2u 3 -2cos(2π/5) -2cos(4π/5) 0 -1 -3 2cos(4π/5) 2cos(2π/5) 0 1
Gu 4 -1 -1 1 0 -4 1 1 -1 0
Hu 5 0 0 -1 1 -5 0 0 1 -1

Ih 점군의 곱셈표
Ag T1g T2g Gg Hg Au T1u T2u Gu Hu Ag T1g T2g Gg Hg Au T1u T2u Gu Hu T1g Ag+T1g+Hg Gg+Hg T2g+Gg+Hg T1g+T2g+Gg+Hg T1u Au+T1u+Hu Gu+Hu T2u+Gu+Hu T1u+T2u+Gu+Hu T2g Gg+Hg Ag+T2g+Hg T1g+Gg+Hg T1g+T2g+Gg+Hg T2u Gu+Hu Au+T2u+Hu T1u+Gu+Hu T1u+T2u+Gu+Hu Gg T2g+Gg+Hg T1g+Gg+Hg Ag+T1g+T2g+Gg+Hg T1g+T2g+Gg+2Hg Gu T2u+Gu+Hu T1u+Gu+Hu Au+T1u+T2u+Gu+Hu T1u+T2u+Gu+2Hu Hg T1g+T2g+Gg+Hg T1g+T2g+Gg+Hg T1g+T2g+Gg+2Hg Ag+T1g+T2g+2Gg+2Hg Hu T1u+T2u+Gu+Hu T1u+T2u+Gu+Hu T1u+T2u+Gu+2Hu Au+T1u+T2u+2Gu+2Hu Au T1u T2u Gu Hu Ag T1g T2g Gg Hg T1u Au+T1u+Hu Gu+Hu T2u+Gu+Hu T1u+T2u+Gu+Hu T1g Ag+T1g+Hg Gg+Hg T2g+Gg+Hg T1g+T2g+Gg+Hg T2u Gu+Hu Au+T2u+Hu T1u+Gu+Hu T1u+T2u+Gu+Hu T2g Gg+Hg Ag+T2g+Hg T1g+Gg+Hg T1g+T2g+Gg+Hg Gu T2u+Gu+Hu T1u+Gu+Hu Au+T1u+T2u+Gu+Hu T1u+T2u+Gu+2Hu Gg T2g+Gg+Hg T1g+Gg+Hg Ag+T1g+T2g+Gg+Hg T1g+T2g+Gg+2Hg Hu T1u+T2u+Gu+Hu T1u+T2u+Gu+Hu T1u+T2u+Gu+2Hu Au+T1u+T2u+2Gu+2Hu Hg T1g+T2g+Gg+Hg T1g+T2g+Gg+Hg T1g+T2g+Gg+2Hg Ag+T1g+T2g+2Gg+2Hg

 인쇄용 Ih 점군 Ih 점군의 인쇄용 지표표 Ih 점군의 인쇄용 곱셈표