Point Group D29h



D29h 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 29C'2 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 29σv
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 1 1 1
A'2 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 1 -1
E'1 2 1.9532 1.8152 1.5922 1.2948 0.9368 0.5351 0.1083 -0.3236 -0.7403 -1.1224 -1.4520 -1.7137 -1.8953 -1.9883 0 2 1.9532 1.8152 1.5922 1.2948 0.9368 0.5351 0.1083 -0.3236 -0.7403 -1.1224 -1.4520 -1.7137 -1.8953 -1.9883 0
E'2 2 1.8152 1.2948 0.5351 -0.3236 -1.1224 -1.7137 -1.9883 -1.8953 -1.4520 -0.7403 0.1083 0.9368 1.5922 1.9532 0 2 1.8152 1.2948 0.5351 -0.3236 -1.1224 -1.7137 -1.9883 -1.8953 -1.4520 -0.7403 0.1083 0.9368 1.5922 1.9532 0
E'3 2 1.5922 0.5351 -0.7403 -1.7137 -1.9883 -1.4520 -0.3236 0.9368 1.8152 1.9532 1.2948 0.1083 -1.1224 -1.8953 0 2 1.5922 0.5351 -0.7403 -1.7137 -1.9883 -1.4520 -0.3236 0.9368 1.8152 1.9532 1.2948 0.1083 -1.1224 -1.8953 0
E'4 2 1.2948 -0.3236 -1.7137 -1.8953 -0.7403 0.9368 1.9532 1.5922 0.1083 -1.4520 -1.9883 -1.1224 0.5351 1.8152 0 2 1.2948 -0.3236 -1.7137 -1.8953 -0.7403 0.9368 1.9532 1.5922 0.1083 -1.4520 -1.9883 -1.1224 0.5351 1.8152 0
E'5 2 0.9368 -1.1224 -1.9883 -0.7403 1.2948 1.9532 0.5351 -1.4520 -1.8953 -0.3236 1.5922 1.8152 0.1083 -1.7137 0 2 0.9368 -1.1224 -1.9883 -0.7403 1.2948 1.9532 0.5351 -1.4520 -1.8953 -0.3236 1.5922 1.8152 0.1083 -1.7137 0
E'6 2 0.5351 -1.7137 -1.4520 0.9368 1.9532 0.1083 -1.8953 -1.1224 1.2948 1.8152 -0.3236 -1.9883 -0.7403 1.5922 0 2 0.5351 -1.7137 -1.4520 0.9368 1.9532 0.1083 -1.8953 -1.1224 1.2948 1.8152 -0.3236 -1.9883 -0.7403 1.5922 0
E'7 2 0.1083 -1.9883 -0.3236 1.9532 0.5351 -1.8953 -0.7403 1.8152 0.9368 -1.7137 -1.1224 1.5922 1.2948 -1.4520 0 2 0.1083 -1.9883 -0.3236 1.9532 0.5351 -1.8953 -0.7403 1.8152 0.9368 -1.7137 -1.1224 1.5922 1.2948 -1.4520 0
E'8 2 -0.3236 -1.8953 0.9368 1.5922 -1.4520 -1.1224 1.8152 0.5351 -1.9883 0.1083 1.9532 -0.7403 -1.7137 1.2948 0 2 -0.3236 -1.8953 0.9368 1.5922 -1.4520 -1.1224 1.8152 0.5351 -1.9883 0.1083 1.9532 -0.7403 -1.7137 1.2948 0
E'9 2 -0.7403 -1.4520 1.8152 0.1083 -1.8953 1.2948 0.9368 -1.9883 0.5351 1.5922 -1.7137 -0.3236 1.9532 -1.1224 0 2 -0.7403 -1.4520 1.8152 0.1083 -1.8953 1.2948 0.9368 -1.9883 0.5351 1.5922 -1.7137 -0.3236 1.9532 -1.1224 0
E'10 2 -1.1224 -0.7403 1.9532 -1.4520 -0.3236 1.8152 -1.7137 0.1083 1.5922 -1.8953 0.5351 1.2948 -1.9883 0.9368 0 2 -1.1224 -0.7403 1.9532 -1.4520 -0.3236 1.8152 -1.7137 0.1083 1.5922 -1.8953 0.5351 1.2948 -1.9883 0.9368 0
E'11 2 -1.4520 0.1083 1.2948 -1.9883 1.5922 -0.3236 -1.1224 1.9532 -1.7137 0.5351 0.9368 -1.8953 1.8152 -0.7403 0 2 -1.4520 0.1083 1.2948 -1.9883 1.5922 -0.3236 -1.1224 1.9532 -1.7137 0.5351 0.9368 -1.8953 1.8152 -0.7403 0
E'12 2 -1.7137 0.9368 0.1083 -1.1224 1.8152 -1.9883 1.5922 -0.7403 -0.3236 1.2948 -1.8953 1.9532 -1.4520 0.5351 0 2 -1.7137 0.9368 0.1083 -1.1224 1.8152 -1.9883 1.5922 -0.7403 -0.3236 1.2948 -1.8953 1.9532 -1.4520 0.5351 0
E'13 2 -1.8953 1.5922 -1.1224 0.5351 0.1083 -0.7403 1.2948 -1.7137 1.9532 -1.9883 1.8152 -1.4520 0.9368 -0.3236 0 2 -1.8953 1.5922 -1.1224 0.5351 0.1083 -0.7403 1.2948 -1.7137 1.9532 -1.9883 1.8152 -1.4520 0.9368 -0.3236 0
E'14 2 -1.9883 1.9532 -1.8953 1.8152 -1.7137 1.5922 -1.4520 1.2948 -1.1224 0.9368 -0.7403 0.5351 -0.3236 0.1083 0 2 -1.9883 1.9532 -1.8953 1.8152 -1.7137 1.5922 -1.4520 1.2948 -1.1224 0.9368 -0.7403 0.5351 -0.3236 0.1083 0
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 -1 -1 -1
A''2 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 -1 1
E''1 2 1.9532 1.8152 1.5922 1.2948 0.9368 0.5351 0.1083 -0.3236 -0.7403 -1.1224 -1.4520 -1.7137 -1.8953 -1.9883 0 -2 -1.9532 -1.8152 -1.5922 -1.2948 -0.9368 -0.5351 -0.1083 0.3236 0.7403 1.1224 1.4520 1.7137 1.8953 1.9883 0
E''2 2 1.8152 1.2948 0.5351 -0.3236 -1.1224 -1.7137 -1.9883 -1.8953 -1.4520 -0.7403 0.1083 0.9368 1.5922 1.9532 0 -2 -1.8152 -1.2948 -0.5351 0.3236 1.1224 1.7137 1.9883 1.8953 1.4520 0.7403 -0.1083 -0.9368 -1.5922 -1.9532 0
E''3 2 1.5922 0.5351 -0.7403 -1.7137 -1.9883 -1.4520 -0.3236 0.9368 1.8152 1.9532 1.2948 0.1083 -1.1224 -1.8953 0 -2 -1.5922 -0.5351 0.7403 1.7137 1.9883 1.4520 0.3236 -0.9368 -1.8152 -1.9532 -1.2948 -0.1083 1.1224 1.8953 0
E''4 2 1.2948 -0.3236 -1.7137 -1.8953 -0.7403 0.9368 1.9532 1.5922 0.1083 -1.4520 -1.9883 -1.1224 0.5351 1.8152 0 -2 -1.2948 0.3236 1.7137 1.8953 0.7403 -0.9368 -1.9532 -1.5922 -0.1083 1.4520 1.9883 1.1224 -0.5351 -1.8152 0
E''5 2 0.9368 -1.1224 -1.9883 -0.7403 1.2948 1.9532 0.5351 -1.4520 -1.8953 -0.3236 1.5922 1.8152 0.1083 -1.7137 0 -2 -0.9368 1.1224 1.9883 0.7403 -1.2948 -1.9532 -0.5351 1.4520 1.8953 0.3236 -1.5922 -1.8152 -0.1083 1.7137 0
E''6 2 0.5351 -1.7137 -1.4520 0.9368 1.9532 0.1083 -1.8953 -1.1224 1.2948 1.8152 -0.3236 -1.9883 -0.7403 1.5922 0 -2 -0.5351 1.7137 1.4520 -0.9368 -1.9532 -0.1083 1.8953 1.1224 -1.2948 -1.8152 0.3236 1.9883 0.7403 -1.5922 0
E''7 2 0.1083 -1.9883 -0.3236 1.9532 0.5351 -1.8953 -0.7403 1.8152 0.9368 -1.7137 -1.1224 1.5922 1.2948 -1.4520 0 -2 -0.1083 1.9883 0.3236 -1.9532 -0.5351 1.8953 0.7403 -1.8152 -0.9368 1.7137 1.1224 -1.5922 -1.2948 1.4520 0
E''8 2 -0.3236 -1.8953 0.9368 1.5922 -1.4520 -1.1224 1.8152 0.5351 -1.9883 0.1083 1.9532 -0.7403 -1.7137 1.2948 0 -2 0.3236 1.8953 -0.9368 -1.5922 1.4520 1.1224 -1.8152 -0.5351 1.9883 -0.1083 -1.9532 0.7403 1.7137 -1.2948 0
E''9 2 -0.7403 -1.4520 1.8152 0.1083 -1.8953 1.2948 0.9368 -1.9883 0.5351 1.5922 -1.7137 -0.3236 1.9532 -1.1224 0 -2 0.7403 1.4520 -1.8152 -0.1083 1.8953 -1.2948 -0.9368 1.9883 -0.5351 -1.5922 1.7137 0.3236 -1.9532 1.1224 0
E''10 2 -1.1224 -0.7403 1.9532 -1.4520 -0.3236 1.8152 -1.7137 0.1083 1.5922 -1.8953 0.5351 1.2948 -1.9883 0.9368 0 -2 1.1224 0.7403 -1.9532 1.4520 0.3236 -1.8152 1.7137 -0.1083 -1.5922 1.8953 -0.5351 -1.2948 1.9883 -0.9368 0
E''11 2 -1.4520 0.1083 1.2948 -1.9883 1.5922 -0.3236 -1.1224 1.9532 -1.7137 0.5351 0.9368 -1.8953 1.8152 -0.7403 0 -2 1.4520 -0.1083 -1.2948 1.9883 -1.5922 0.3236 1.1224 -1.9532 1.7137 -0.5351 -0.9368 1.8953 -1.8152 0.7403 0
E''12 2 -1.7137 0.9368 0.1083 -1.1224 1.8152 -1.9883 1.5922 -0.7403 -0.3236 1.2948 -1.8953 1.9532 -1.4520 0.5351 0 -2 1.7137 -0.9368 -0.1083 1.1224 -1.8152 1.9883 -1.5922 0.7403 0.3236 -1.2948 1.8953 -1.9532 1.4520 -0.5351 0
E''13 2 -1.8953 1.5922 -1.1224 0.5351 0.1083 -0.7403 1.2948 -1.7137 1.9532 -1.9883 1.8152 -1.4520 0.9368 -0.3236 0 -2 1.8953 -1.5922 1.1224 -0.5351 -0.1083 0.7403 -1.2948 1.7137 -1.9532 1.9883 -1.8152 1.4520 -0.9368 0.3236 0
E''14 2 -1.9883 1.9532 -1.8953 1.8152 -1.7137 1.5922 -1.4520 1.2948 -1.1224 0.9368 -0.7403 0.5351 -0.3236 0.1083 0 -2 1.9883 -1.9532 1.8953 -1.8152 1.7137 -1.5922 1.4520 -1.2948 1.1224 -0.9368 0.7403 -0.5351 0.3236 -0.1083 0
View A
View B
✅


Additional information

Number of symmetry elements h = 116
Number of classes, irreps n = 32
Abelian group no
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 29C'2 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 29σv



Genrate representation from irreducible representations


A'1 A'2 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''1 A''2 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: 1

Binary products
⊙ A'1 A'2 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''1 A''2 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'1
Characters of reducible representation
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 29C'2 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 29σv
5 11.263 1.755 23.857 24.650 33.369 0.001 5.603 47.056 17.149 6.787 14.520 21.958 41.544 1.490 1 25 28.686 0.456 8.319 48.509 14.262 3.884 19.072 23.617 37.714 0.366 3.278 44.702 19.762 10.374 1