Point Group S29



S29 E 2S29 2(C29)2 2(S29)3 2(C29)4 2(S29)5 2(C29)6 2(S29)7 2(C29)8 2(S29)9 2(C29)10 2(S29)11 2(C29)12 2(S29)13 2(C29)14
A 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
B 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1
E1* 2 2cos(2π/29) 2cos(4π/29) 2cos(6π/29) 2cos(8π/29) 2cos(10π/29) 2cos(12π/29) 2cos(14π/29) -2cos(12π/29) -2cos(10π/29) -2cos(8π/29) -2cos(6π/29) -2cos(4π/29) -2cos(2π/29)
E2* 2 2cos(4π/29) 2cos(8π/29) 2cos(12π/29) -2cos(12π/29) -2cos(8π/29) -2cos(4π/29) -2cos(2π/29) -2cos(6π/29) -2cos(10π/29) 2cos(14π/29) 2cos(10π/29) 2cos(6π/29) 2cos(2π/29)
E3* 2 2cos(6π/29) 2cos(12π/29) -2cos(10π/29) -2cos(4π/29) -2cos(6π/29) -2cos(12π/29) 2cos(10π/29) 2cos(4π/29) 2cos(2π/29) 2cos(8π/29) 2cos(14π/29) -2cos(8π/29) -2cos(2π/29)
E4* 2 2cos(8π/29) -2cos(12π/29) -2cos(4π/29) -2cos(2π/29) -2cos(10π/29) 2cos(10π/29) 2cos(2π/29) 2cos(6π/29) 2cos(14π/29) -2cos(6π/29) -2cos(8π/29) 2cos(12π/29) 2cos(4π/29)
E5* 2 2cos(10π/29) -2cos(8π/29) -2cos(10π/29) 2cos(8π/29) 2cos(2π/29) 2cos(12π/29) -2cos(6π/29) -2cos(2π/29) -2cos(12π/29) 2cos(6π/29) 2cos(4π/29) 2cos(14π/29) -2cos(4π/29)
E6* 2 2cos(12π/29) -2cos(4π/29) -2cos(6π/29) 2cos(10π/29) 2cos(2π/29) 2cos(14π/29) -2cos(2π/29) -2cos(8π/29) 2cos(8π/29) 2cos(4π/29) -2cos(12π/29) -2cos(10π/29) 2cos(6π/29)
E7* 2 2cos(14π/29) -2cos(12π/29) 2cos(2π/29) 2cos(12π/29) -2cos(2π/29) -2cos(10π/29) 2cos(4π/29) 2cos(10π/29) -2cos(4π/29) -2cos(8π/29) 2cos(6π/29) 2cos(8π/29) -2cos(6π/29)
E8* 2 -2cos(12π/29) -2cos(2π/29) 2cos(10π/29) 2cos(6π/29) -2cos(6π/29) -2cos(8π/29) 2cos(4π/29) 2cos(12π/29) 2cos(14π/29) 2cos(2π/29) -2cos(10π/29) -2cos(4π/29) 2cos(8π/29)
E9* 2 -2cos(10π/29) -2cos(6π/29) 2cos(4π/29) 2cos(14π/29) -2cos(2π/29) 2cos(8π/29) 2cos(10π/29) 2cos(12π/29) 2cos(6π/29) -2cos(4π/29) -2cos(12π/29) 2cos(2π/29) -2cos(8π/29)
E10* 2 -2cos(8π/29) -2cos(10π/29) 2cos(2π/29) -2cos(6π/29) -2cos(12π/29) 2cos(4π/29) -2cos(4π/29) 2cos(14π/29) 2cos(6π/29) -2cos(2π/29) 2cos(12π/29) 2cos(8π/29) 2cos(10π/29)
E11* 2 -2cos(6π/29) 2cos(14π/29) 2cos(8π/29) 2cos(6π/29) -2cos(12π/29) -2cos(8π/29) 2cos(2π/29) -2cos(4π/29) 2cos(12π/29) 2cos(10π/29) -2cos(2π/29) 2cos(4π/29) -2cos(10π/29)
E12* 2 -2cos(4π/29) 2cos(10π/29) 2cos(14π/29) -2cos(8π/29) 2cos(4π/29) 2cos(6π/29) -2cos(10π/29) -2cos(12π/29) 2cos(8π/29) -2cos(2π/29) 2cos(2π/29) -2cos(6π/29) 2cos(12π/29)
E13* 2 -2cos(2π/29) 2cos(6π/29) -2cos(8π/29) 2cos(12π/29) 2cos(14π/29) -2cos(10π/29) 2cos(8π/29) -2cos(4π/29) 2cos(2π/29) 2cos(4π/29) -2cos(6π/29) 2cos(10π/29) -2cos(12π/29)
Math View
Phys View A
Phys View B
Chem View A
✅
Chem View B


Additional information

Number of symmetry elements h = 29
Number of classes, irreps n = 29
Number of real-valued irreducible representations n = 15
Abelian group yes
Optical Isomerism (Chirality) no
Polar no
Parity no


Reduce representation to irreducible representations


E 2S29 2(C29)2 2(S29)3 2(C29)4 2(S29)5 2(C29)6 2(S29)7 2(C29)8 2(S29)9 2(C29)10 2(S29)11 2(C29)12 2(S29)13 2(C29)14



Genrate representation from irreducible representations


A B E1* E2* E3* E4* E5* E6* E7* E8* E9* E10* E11* E12* E13*



Direct products of irreducible representations




Error: Reduction failed

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

Binary products
⊙ A B E1* E2* E3* E4* E5* E6* E7* E8* E9* E10* E11* E12* E13*
A A
B
Characters of reducible representation
E S29 (C29)2 (S29)3 (C29)4 (S29)5 (C29)6 (S29)7 (C29)8 (S29)9 (C29)10 (S29)11 (C29)12 (S29)13 (C29)14 (S29)15 (C29)16 (S29)17 (C29)18 (S29)19 (C29)20 (S29)21 (C29)22 (S29)23 (C29)24 (S29)25 (C29)26 (S29)27 (C29)28
1 -1.000 1.000 -1.000 1.000 -1.000 1.000 -1.000 1.000 -1.000 1.000 -1.000 1.000 -1.000 1.000 -1.000 1.000 -1.000 1.000 -1.000 1.000 -1.000 1.000 -1.000 1.000 -1.000 1.000 -1.000 1.000