Point Group C29h



C29h E 2C29 2(C29)2 2(C29)3 2(C29)4 2(C29)5 2(C29)6 2(C29)7 2(C29)8 2(C29)9 2(C29)10 2(C29)11 2(C29)12 2(C29)13 2(C29)14 σh 2S29 2(S29)27 2(S29)3 2(S29)25 2(S29)5 2(S29)23 2(S29)7 2(S29)21 2(S29)9 2(S29)19 2(S29)11 2(S29)17 2(S29)13 2(S29)15
A' 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
E'1* 2 2cos(2π/29) 2cos(4π/29) 2cos(6π/29) 2cos(8π/29) 2cos(10π/29) 2cos(12π/29) 2cos(14π/29) 2cos(16π/29) 2cos(18π/29) 2cos(20π/29) 2cos(22π/29) 2cos(24π/29) 2cos(26π/29) 2cos(28π/29) 2 2cos(2π/29) 2cos(4π/29) 2cos(6π/29) 2cos(8π/29) 2cos(10π/29) 2cos(12π/29) 2cos(14π/29) 2cos(16π/29) 2cos(18π/29) 2cos(20π/29) 2cos(22π/29) 2cos(24π/29) 2cos(26π/29) 2cos(28π/29)
E'2* 2 2cos(4π/29) 2cos(8π/29) 2cos(12π/29) 2cos(16π/29) 2cos(20π/29) 2cos(24π/29) 2cos(28π/29) 2cos(26π/29) 2cos(22π/29) 2cos(18π/29) 2cos(14π/29) 2cos(10π/29) 2cos(6π/29) 2cos(2π/29) 2 2cos(4π/29) 2cos(8π/29) 2cos(12π/29) 2cos(16π/29) 2cos(20π/29) 2cos(24π/29) 2cos(28π/29) 2cos(26π/29) 2cos(22π/29) 2cos(18π/29) 2cos(14π/29) 2cos(10π/29) 2cos(6π/29) 2cos(2π/29)
E'3* 2 2cos(6π/29) 2cos(12π/29) 2cos(18π/29) 2cos(24π/29) 2cos(28π/29) 2cos(22π/29) 2cos(16π/29) 2cos(10π/29) 2cos(4π/29) 2cos(2π/29) 2cos(8π/29) 2cos(14π/29) 2cos(20π/29) 2cos(26π/29) 2 2cos(6π/29) 2cos(12π/29) 2cos(18π/29) 2cos(24π/29) 2cos(28π/29) 2cos(22π/29) 2cos(16π/29) 2cos(10π/29) 2cos(4π/29) 2cos(2π/29) 2cos(8π/29) 2cos(14π/29) 2cos(20π/29) 2cos(26π/29)
E'4* 2 2cos(8π/29) 2cos(16π/29) 2cos(24π/29) 2cos(26π/29) 2cos(18π/29) 2cos(10π/29) 2cos(2π/29) 2cos(6π/29) 2cos(14π/29) 2cos(22π/29) 2cos(28π/29) 2cos(20π/29) 2cos(12π/29) 2cos(4π/29) 2 2cos(8π/29) 2cos(16π/29) 2cos(24π/29) 2cos(26π/29) 2cos(18π/29) 2cos(10π/29) 2cos(2π/29) 2cos(6π/29) 2cos(14π/29) 2cos(22π/29) 2cos(28π/29) 2cos(20π/29) 2cos(12π/29) 2cos(4π/29)
E'5* 2 2cos(10π/29) 2cos(20π/29) 2cos(28π/29) 2cos(18π/29) 2cos(8π/29) 2cos(2π/29) 2cos(12π/29) 2cos(22π/29) 2cos(26π/29) 2cos(16π/29) 2cos(6π/29) 2cos(4π/29) 2cos(14π/29) 2cos(24π/29) 2 2cos(10π/29) 2cos(20π/29) 2cos(28π/29) 2cos(18π/29) 2cos(8π/29) 2cos(2π/29) 2cos(12π/29) 2cos(22π/29) 2cos(26π/29) 2cos(16π/29) 2cos(6π/29) 2cos(4π/29) 2cos(14π/29) 2cos(24π/29)
E'6* 2 2cos(12π/29) 2cos(24π/29) 2cos(22π/29) 2cos(10π/29) 2cos(2π/29) 2cos(14π/29) 2cos(26π/29) 2cos(20π/29) 2cos(8π/29) 2cos(4π/29) 2cos(16π/29) 2cos(28π/29) 2cos(18π/29) 2cos(6π/29) 2 2cos(12π/29) 2cos(24π/29) 2cos(22π/29) 2cos(10π/29) 2cos(2π/29) 2cos(14π/29) 2cos(26π/29) 2cos(20π/29) 2cos(8π/29) 2cos(4π/29) 2cos(16π/29) 2cos(28π/29) 2cos(18π/29) 2cos(6π/29)
E'7* 2 2cos(14π/29) 2cos(28π/29) 2cos(16π/29) 2cos(2π/29) 2cos(12π/29) 2cos(26π/29) 2cos(18π/29) 2cos(4π/29) 2cos(10π/29) 2cos(24π/29) 2cos(20π/29) 2cos(6π/29) 2cos(8π/29) 2cos(22π/29) 2 2cos(14π/29) 2cos(28π/29) 2cos(16π/29) 2cos(2π/29) 2cos(12π/29) 2cos(26π/29) 2cos(18π/29) 2cos(4π/29) 2cos(10π/29) 2cos(24π/29) 2cos(20π/29) 2cos(6π/29) 2cos(8π/29) 2cos(22π/29)
E'8* 2 2cos(16π/29) 2cos(26π/29) 2cos(10π/29) 2cos(6π/29) 2cos(22π/29) 2cos(20π/29) 2cos(4π/29) 2cos(12π/29) 2cos(28π/29) 2cos(14π/29) 2cos(2π/29) 2cos(18π/29) 2cos(24π/29) 2cos(8π/29) 2 2cos(16π/29) 2cos(26π/29) 2cos(10π/29) 2cos(6π/29) 2cos(22π/29) 2cos(20π/29) 2cos(4π/29) 2cos(12π/29) 2cos(28π/29) 2cos(14π/29) 2cos(2π/29) 2cos(18π/29) 2cos(24π/29) 2cos(8π/29)
E'9* 2 2cos(18π/29) 2cos(22π/29) 2cos(4π/29) 2cos(14π/29) 2cos(26π/29) 2cos(8π/29) 2cos(10π/29) 2cos(28π/29) 2cos(12π/29) 2cos(6π/29) 2cos(24π/29) 2cos(16π/29) 2cos(2π/29) 2cos(20π/29) 2 2cos(18π/29) 2cos(22π/29) 2cos(4π/29) 2cos(14π/29) 2cos(26π/29) 2cos(8π/29) 2cos(10π/29) 2cos(28π/29) 2cos(12π/29) 2cos(6π/29) 2cos(24π/29) 2cos(16π/29) 2cos(2π/29) 2cos(20π/29)
E'10* 2 2cos(20π/29) 2cos(18π/29) 2cos(2π/29) 2cos(22π/29) 2cos(16π/29) 2cos(4π/29) 2cos(24π/29) 2cos(14π/29) 2cos(6π/29) 2cos(26π/29) 2cos(12π/29) 2cos(8π/29) 2cos(28π/29) 2cos(10π/29) 2 2cos(20π/29) 2cos(18π/29) 2cos(2π/29) 2cos(22π/29) 2cos(16π/29) 2cos(4π/29) 2cos(24π/29) 2cos(14π/29) 2cos(6π/29) 2cos(26π/29) 2cos(12π/29) 2cos(8π/29) 2cos(28π/29) 2cos(10π/29)
E'11* 2 2cos(22π/29) 2cos(14π/29) 2cos(8π/29) 2cos(28π/29) 2cos(6π/29) 2cos(16π/29) 2cos(20π/29) 2cos(2π/29) 2cos(24π/29) 2cos(12π/29) 2cos(10π/29) 2cos(26π/29) 2cos(4π/29) 2cos(18π/29) 2 2cos(22π/29) 2cos(14π/29) 2cos(8π/29) 2cos(28π/29) 2cos(6π/29) 2cos(16π/29) 2cos(20π/29) 2cos(2π/29) 2cos(24π/29) 2cos(12π/29) 2cos(10π/29) 2cos(26π/29) 2cos(4π/29) 2cos(18π/29)
E'12* 2 2cos(24π/29) 2cos(10π/29) 2cos(14π/29) 2cos(20π/29) 2cos(4π/29) 2cos(28π/29) 2cos(6π/29) 2cos(18π/29) 2cos(16π/29) 2cos(8π/29) 2cos(26π/29) 2cos(2π/29) 2cos(22π/29) 2cos(12π/29) 2 2cos(24π/29) 2cos(10π/29) 2cos(14π/29) 2cos(20π/29) 2cos(4π/29) 2cos(28π/29) 2cos(6π/29) 2cos(18π/29) 2cos(16π/29) 2cos(8π/29) 2cos(26π/29) 2cos(2π/29) 2cos(22π/29) 2cos(12π/29)
E'13* 2 2cos(26π/29) 2cos(6π/29) 2cos(20π/29) 2cos(12π/29) 2cos(14π/29) 2cos(18π/29) 2cos(8π/29) 2cos(24π/29) 2cos(2π/29) 2cos(28π/29) 2cos(4π/29) 2cos(22π/29) 2cos(10π/29) 2cos(16π/29) 2 2cos(26π/29) 2cos(6π/29) 2cos(20π/29) 2cos(12π/29) 2cos(14π/29) 2cos(18π/29) 2cos(8π/29) 2cos(24π/29) 2cos(2π/29) 2cos(28π/29) 2cos(4π/29) 2cos(22π/29) 2cos(10π/29) 2cos(16π/29)
E'14* 2 2cos(28π/29) 2cos(2π/29) 2cos(26π/29) 2cos(4π/29) 2cos(24π/29) 2cos(6π/29) 2cos(22π/29) 2cos(8π/29) 2cos(20π/29) 2cos(10π/29) 2cos(18π/29) 2cos(12π/29) 2cos(16π/29) 2cos(14π/29) 2 2cos(28π/29) 2cos(2π/29) 2cos(26π/29) 2cos(4π/29) 2cos(24π/29) 2cos(6π/29) 2cos(22π/29) 2cos(8π/29) 2cos(20π/29) 2cos(10π/29) 2cos(18π/29) 2cos(12π/29) 2cos(16π/29) 2cos(14π/29)
A'' 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
E''1* 2 2cos(2π/29) 2cos(4π/29) 2cos(6π/29) 2cos(8π/29) 2cos(10π/29) 2cos(12π/29) 2cos(14π/29) 2cos(16π/29) 2cos(18π/29) 2cos(20π/29) 2cos(22π/29) 2cos(24π/29) 2cos(26π/29) 2cos(28π/29) -2 -2cos(2π/29) -2cos(4π/29) -2cos(6π/29) -2cos(8π/29) -2cos(10π/29) -2cos(12π/29) -2cos(14π/29) -2cos(16π/29) -2cos(18π/29) -2cos(20π/29) -2cos(22π/29) -2cos(24π/29) -2cos(26π/29) -2cos(28π/29)
E''2* 2 2cos(4π/29) 2cos(8π/29) 2cos(12π/29) 2cos(16π/29) 2cos(20π/29) 2cos(24π/29) 2cos(28π/29) 2cos(26π/29) 2cos(22π/29) 2cos(18π/29) 2cos(14π/29) 2cos(10π/29) 2cos(6π/29) 2cos(2π/29) -2 -2cos(4π/29) -2cos(8π/29) -2cos(12π/29) -2cos(16π/29) -2cos(20π/29) -2cos(24π/29) -2cos(28π/29) -2cos(26π/29) -2cos(22π/29) -2cos(18π/29) -2cos(14π/29) -2cos(10π/29) -2cos(6π/29) -2cos(2π/29)
E''3* 2 2cos(6π/29) 2cos(12π/29) 2cos(18π/29) 2cos(24π/29) 2cos(28π/29) 2cos(22π/29) 2cos(16π/29) 2cos(10π/29) 2cos(4π/29) 2cos(2π/29) 2cos(8π/29) 2cos(14π/29) 2cos(20π/29) 2cos(26π/29) -2 -2cos(6π/29) -2cos(12π/29) -2cos(18π/29) -2cos(24π/29) -2cos(28π/29) -2cos(22π/29) -2cos(16π/29) -2cos(10π/29) -2cos(4π/29) -2cos(2π/29) -2cos(8π/29) -2cos(14π/29) -2cos(20π/29) -2cos(26π/29)
E''4* 2 2cos(8π/29) 2cos(16π/29) 2cos(24π/29) 2cos(26π/29) 2cos(18π/29) 2cos(10π/29) 2cos(2π/29) 2cos(6π/29) 2cos(14π/29) 2cos(22π/29) 2cos(28π/29) 2cos(20π/29) 2cos(12π/29) 2cos(4π/29) -2 -2cos(8π/29) -2cos(16π/29) -2cos(24π/29) -2cos(26π/29) -2cos(18π/29) -2cos(10π/29) -2cos(2π/29) -2cos(6π/29) -2cos(14π/29) -2cos(22π/29) -2cos(28π/29) -2cos(20π/29) -2cos(12π/29) -2cos(4π/29)
E''5* 2 2cos(10π/29) 2cos(20π/29) 2cos(28π/29) 2cos(18π/29) 2cos(8π/29) 2cos(2π/29) 2cos(12π/29) 2cos(22π/29) 2cos(26π/29) 2cos(16π/29) 2cos(6π/29) 2cos(4π/29) 2cos(14π/29) 2cos(24π/29) -2 -2cos(10π/29) -2cos(20π/29) -2cos(28π/29) -2cos(18π/29) -2cos(8π/29) -2cos(2π/29) -2cos(12π/29) -2cos(22π/29) -2cos(26π/29) -2cos(16π/29) -2cos(6π/29) -2cos(4π/29) -2cos(14π/29) -2cos(24π/29)
E''6* 2 2cos(12π/29) 2cos(24π/29) 2cos(22π/29) 2cos(10π/29) 2cos(2π/29) 2cos(14π/29) 2cos(26π/29) 2cos(20π/29) 2cos(8π/29) 2cos(4π/29) 2cos(16π/29) 2cos(28π/29) 2cos(18π/29) 2cos(6π/29) -2 -2cos(12π/29) -2cos(24π/29) -2cos(22π/29) -2cos(10π/29) -2cos(2π/29) -2cos(14π/29) -2cos(26π/29) -2cos(20π/29) -2cos(8π/29) -2cos(4π/29) -2cos(16π/29) -2cos(28π/29) -2cos(18π/29) -2cos(6π/29)
E''7* 2 2cos(14π/29) 2cos(28π/29) 2cos(16π/29) 2cos(2π/29) 2cos(12π/29) 2cos(26π/29) 2cos(18π/29) 2cos(4π/29) 2cos(10π/29) 2cos(24π/29) 2cos(20π/29) 2cos(6π/29) 2cos(8π/29) 2cos(22π/29) -2 -2cos(14π/29) -2cos(28π/29) -2cos(16π/29) -2cos(2π/29) -2cos(12π/29) -2cos(26π/29) -2cos(18π/29) -2cos(4π/29) -2cos(10π/29) -2cos(24π/29) -2cos(20π/29) -2cos(6π/29) -2cos(8π/29) -2cos(22π/29)
E''8* 2 2cos(16π/29) 2cos(26π/29) 2cos(10π/29) 2cos(6π/29) 2cos(22π/29) 2cos(20π/29) 2cos(4π/29) 2cos(12π/29) 2cos(28π/29) 2cos(14π/29) 2cos(2π/29) 2cos(18π/29) 2cos(24π/29) 2cos(8π/29) -2 -2cos(16π/29) -2cos(26π/29) -2cos(10π/29) -2cos(6π/29) -2cos(22π/29) -2cos(20π/29) -2cos(4π/29) -2cos(12π/29) -2cos(28π/29) -2cos(14π/29) -2cos(2π/29) -2cos(18π/29) -2cos(24π/29) -2cos(8π/29)
E''9* 2 2cos(18π/29) 2cos(22π/29) 2cos(4π/29) 2cos(14π/29) 2cos(26π/29) 2cos(8π/29) 2cos(10π/29) 2cos(28π/29) 2cos(12π/29) 2cos(6π/29) 2cos(24π/29) 2cos(16π/29) 2cos(2π/29) 2cos(20π/29) -2 -2cos(18π/29) -2cos(22π/29) -2cos(4π/29) -2cos(14π/29) -2cos(26π/29) -2cos(8π/29) -2cos(10π/29) -2cos(28π/29) -2cos(12π/29) -2cos(6π/29) -2cos(24π/29) -2cos(16π/29) -2cos(2π/29) -2cos(20π/29)
E''10* 2 2cos(20π/29) 2cos(18π/29) 2cos(2π/29) 2cos(22π/29) 2cos(16π/29) 2cos(4π/29) 2cos(24π/29) 2cos(14π/29) 2cos(6π/29) 2cos(26π/29) 2cos(12π/29) 2cos(8π/29) 2cos(28π/29) 2cos(10π/29) -2 -2cos(20π/29) -2cos(18π/29) -2cos(2π/29) -2cos(22π/29) -2cos(16π/29) -2cos(4π/29) -2cos(24π/29) -2cos(14π/29) -2cos(6π/29) -2cos(26π/29) -2cos(12π/29) -2cos(8π/29) -2cos(28π/29) -2cos(10π/29)
E''11* 2 2cos(22π/29) 2cos(14π/29) 2cos(8π/29) 2cos(28π/29) 2cos(6π/29) 2cos(16π/29) 2cos(20π/29) 2cos(2π/29) 2cos(24π/29) 2cos(12π/29) 2cos(10π/29) 2cos(26π/29) 2cos(4π/29) 2cos(18π/29) -2 -2cos(22π/29) -2cos(14π/29) -2cos(8π/29) -2cos(28π/29) -2cos(6π/29) -2cos(16π/29) -2cos(20π/29) -2cos(2π/29) -2cos(24π/29) -2cos(12π/29) -2cos(10π/29) -2cos(26π/29) -2cos(4π/29) -2cos(18π/29)
E''12* 2 2cos(24π/29) 2cos(10π/29) 2cos(14π/29) 2cos(20π/29) 2cos(4π/29) 2cos(28π/29) 2cos(6π/29) 2cos(18π/29) 2cos(16π/29) 2cos(8π/29) 2cos(26π/29) 2cos(2π/29) 2cos(22π/29) 2cos(12π/29) -2 -2cos(24π/29) -2cos(10π/29) -2cos(14π/29) -2cos(20π/29) -2cos(4π/29) -2cos(28π/29) -2cos(6π/29) -2cos(18π/29) -2cos(16π/29) -2cos(8π/29) -2cos(26π/29) -2cos(2π/29) -2cos(22π/29) -2cos(12π/29)
E''13* 2 2cos(26π/29) 2cos(6π/29) 2cos(20π/29) 2cos(12π/29) 2cos(14π/29) 2cos(18π/29) 2cos(8π/29) 2cos(24π/29) 2cos(2π/29) 2cos(28π/29) 2cos(4π/29) 2cos(22π/29) 2cos(10π/29) 2cos(16π/29) -2 -2cos(26π/29) -2cos(6π/29) -2cos(20π/29) -2cos(12π/29) -2cos(14π/29) -2cos(18π/29) -2cos(8π/29) -2cos(24π/29) -2cos(2π/29) -2cos(28π/29) -2cos(4π/29) -2cos(22π/29) -2cos(10π/29) -2cos(16π/29)
E''14* 2 2cos(28π/29) 2cos(2π/29) 2cos(26π/29) 2cos(4π/29) 2cos(24π/29) 2cos(6π/29) 2cos(22π/29) 2cos(8π/29) 2cos(20π/29) 2cos(10π/29) 2cos(18π/29) 2cos(12π/29) 2cos(16π/29) 2cos(14π/29) -2 -2cos(28π/29) -2cos(2π/29) -2cos(26π/29) -2cos(4π/29) -2cos(24π/29) -2cos(6π/29) -2cos(22π/29) -2cos(8π/29) -2cos(20π/29) -2cos(10π/29) -2cos(18π/29) -2cos(12π/29) -2cos(16π/29) -2cos(14π/29)
Math View
Phys View A
Phys View B
Chem View A
✅
Chem View B


Additional information

Number of symmetry elements h = 58
Number of classes, irreps n = 58
Number of real-valued irreducible representations n = 30
Abelian group yes
Optical Isomerism (Chirality) no
Polar no
Parity no


Reduce representation to irreducible representations


E 2C29 2(C29)2 2(C29)3 2(C29)4 2(C29)5 2(C29)6 2(C29)7 2(C29)8 2(C29)9 2(C29)10 2(C29)11 2(C29)12 2(C29)13 2(C29)14 σh 2S29 2(S29)27 2(S29)3 2(S29)25 2(S29)5 2(S29)23 2(S29)7 2(S29)21 2(S29)9 2(S29)19 2(S29)11 2(S29)17 2(S29)13 2(S29)15



Genrate representation from irreducible representations


A' E'1* E'2* E'3* E'4* E'5* E'6* E'7* E'8* E'9* E'10* E'11* E'12* E'13* E'14* A'' E''1* E''2* E''3* E''4* E''5* E''6* E''7* E''8* E''9* E''10* E''11* E''12* E''13* E''14*



Direct products of irreducible representations




Error: Reduction failed

Reduction to integer numbers for irreducible representations failed.
Error Code: 2

Binary products
⊙ A' E'1* E'2* E'3* E'4* E'5* E'6* E'7* E'8* E'9* E'10* E'11* E'12* E'13* E'14* A'' E''1* E''2* E''3* E''4* E''5* E''6* E''7* E''8* E''9* E''10* E''11* E''12* E''13* E''14*
A'
Characters of reducible representation
E C29 (C29)2 (C29)3 (C29)4 (C29)5 (C29)6 (C29)7 (C29)8 (C29)9 (C29)10 (C29)11 (C29)12 (C29)13 (C29)14 (C29)15 (C29)16 (C29)17 (C29)18 (C29)19 (C29)20 (C29)21 (C29)22 (C29)23 (C29)24 (C29)25 (C29)26 (C29)27 (C29)28 σh S29 (S29)31 (S29)3 (S29)33 (S29)5 (S29)35 (S29)7 (S29)37 (S29)9 (S29)39 (S29)11 (S29)41 (S29)13 (S29)43 (S29)15 (S29)45 (S29)17 (S29)47 (S29)19 (S29)49 (S29)21 (S29)51 (S29)23 (S29)53 (S29)25 (S29)55 (S29)27 (S29)57
0 -9.235 11.384 4.286 13.953 -5.889 -8.503 -23.736 -25.431 -19.786 -15.991 4.352 2.031 16.641 -0.111 0.196 14.520 11.263 41.544 24.650 47.056 17.149 23.857 1.490 1.755 6.787 5.603 33.369 21.958 25 44.702 14.262 19.072 0.366 0.456 10.374 8.319 37.714 23.617 48.509 19.762 28.686 3.278 3.884 3.884 3.278 28.686 19.762 48.509 23.617 37.714 8.319 10.374 0.456 0.366 19.072 14.262 44.702