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d5d - Point Group Symmetry Character Tables

D5d Point Group

not Abelian, 8(12) irreducible representations
Subgroups of D5d point group: Cs, Ci, C2, C5, D5, C5v, S10

Character table for D5d point group

E2C52(C5)25C'2i2(S10)32S10dlinear,
rotations
quadratic
A1g11111111x2+y2, z2
A2g111-1111-1Rz
E1g22cos(2π/5)2cos(4π/5)022cos(2π/5)2cos(4π/5)0(Rx, Ry)(xz, yz)
E2g22cos(4π/5)2cos(2π/5)022cos(4π/5)2cos(2π/5)0(x2-y2, xy)
A1u1111-1-1-1-1
A2u111-1-1-1-11z
E1u22cos(2π/5)2cos(4π/5)0-2-2cos(2π/5)-2cos(4π/5)0(x, y)
E2u22cos(4π/5)2cos(2π/5)0-2-2cos(4π/5)-2cos(2π/5)0

Product table for D5d point group

 A1gA2gE1gE2gA1uA2uE1uE2u
A1gA1gA2gE1gE2gA1uA2uE1uE2u
A2gA2gA1gE1gE2gA2uA1uE1uE2u
E1gE1gE1gA1g+A2g+E2gE1g+E2gE1uE1uA1u+A2u+E2uE1u+E2u
E2gE2gE2gE1g+E2gA1g+A2g+E2gE2uE2uE1u+E2uA1u+A2u+E2u
A1uA1uA2uE1uA2uA1gA2gE1gE2g
A2uA2uA1uE1uE2uA2gA1gE1gE2g
E1uE1uE1uA1u+A2u+E2uE1u+E2uE1gE1gA1g+A2g+E2gE1g+E2g
E2uE2uE2uE1u+E2uA1u+A2u+E2uE2gE2gE1g+E2gA1g+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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