Point Group S11



S11 E 2(C11)2 2(C11)4 i 2(S11)4 2(S11)2 S1
Ag 1 1 1 1 1 1 1
E1g* 2 2cos(2π/5) 2cos(4π/5) 2 2cos(2π/5) 2cos(4π/5) 2cos(4π/5)
E2g* 2 2cos(4π/5) 2cos(2π/5) 2 2cos(4π/5) 2cos(2π/5) 2cos(2π/5)
Au 1 1 1 -1 -1 -1 -1
E1u* 2 2cos(2π/5) 2cos(4π/5) -2 -2cos(2π/5) -2cos(4π/5) -2cos(4π/5)
E2u* 2 2cos(4π/5) 2cos(2π/5) -2 -2cos(4π/5) -2cos(2π/5) -2cos(2π/5)
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Additional information

Number of symmetry elements h = 11
Number of classes, irreps n = 11
Number of real-valued irreducible representations n = 6
Abelian group yes
Optical Isomerism (Chirality) no
Polar no
Parity yes


Reduce representation to irreducible representations


E 2(C11)2 2(C11)4 i 2(S11)4 2(S11)2 S1



Genrate representation from irreducible representations


Ag E1g* E2g* Au E1u* E2u*



Direct products of irreducible representations




Error: Reduction failed

Reduction to integer numbers for irreducible representations failed.
Error Code: 1

Binary products
⊙ Ag E1g* E2g* Au E1u* E2u*
Ag
Characters of reducible representation
E (C11)2 (C11)4 (C11)6 (C11)8 i (S11)7 (S11)9 S1 (S11)2 (S11)4
1 1.000 1.000 1.000 1.000 1 1.000 1.000 1.000 1.000 1