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

Character table
E 2C5 2(C5)2 5C'2 i 2(S10)3 2S10 d linear,
rotations
quadratic
A1g 1 1 1 1 1 1 1 1 x2+y2, z2
A2g 1 1 1 -1 1 1 1 -1 Rz
E1g 2 2cos(2π/5) 2cos(4π/5) 0 2 2cos(2π/5) 2cos(4π/5) 0 (Rx, Ry) (xz, yz)
E2g 2 2cos(4π/5) 2cos(2π/5) 0 2 2cos(4π/5) 2cos(2π/5) 0 (x2-y2, xy)
A1u 1 1 1 1 -1 -1 -1 -1
A2u 1 1 1 -1 -1 -1 -1 1 z
E1u 2 2cos(2π/5) 2cos(4π/5) 0 -2 -2cos(2π/5) -2cos(4π/5) 0 (x, y)
E2u 2 2cos(4π/5) 2cos(2π/5) 0 -2 -2cos(4π/5) -2cos(2π/5) 0

Product table
 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

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