Point Group D29d



D29d 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 i 2(S58)27 2(S58)25 2(S58)23 2(S58)21 2(S58)19 2(S58)17 2(S58)15 2(S58)13 2(S58)11 2(S58)9 2(S58)7 2(S58)5 2(S58)3 2S58 29σd
A1g 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
A2g 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
E1g 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
E2g 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
E3g 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
E4g 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
E5g 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
E6g 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
E7g 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
E8g 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
E9g 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
E10g 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
E11g 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
E12g 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
E13g 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
E14g 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
A1u 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
A2u 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
E1u 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
E2u 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
E3u 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
E4u 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
E5u 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
E6u 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
E7u 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
E8u 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
E9u 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
E10u 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
E11u 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
E12u 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
E13u 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
E14u 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 yes


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 i 2(S58)27 2(S58)25 2(S58)23 2(S58)21 2(S58)19 2(S58)17 2(S58)15 2(S58)13 2(S58)11 2(S58)9 2(S58)7 2(S58)5 2(S58)3 2S58 29σd



Genrate representation from irreducible representations


A1g A2g E1g E2g E3g E4g E5g E6g E7g E8g E9g E10g E11g E12g E13g E14g A1u A2u E1u E2u E3u E4u E5u E6u E7u E8u E9u E10u E11u E12u E13u E14u



Direct products of irreducible representations




Error: Reduction failed

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

Binary products
⊙ A1g A2g E1g E2g E3g E4g E5g E6g E7g E8g E9g E10g E11g E12g E13g E14g A1u A2u E1u E2u E3u E4u E5u E6u E7u E8u E9u E10u E11u E12u E13u E14u
A1g
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 i 2(S58)27 2(S58)25 2(S58)23 2(S58)21 2(S58)19 2(S58)17 2(S58)15 2(S58)13 2(S58)11 2(S58)9 2(S58)7 2(S58)5 2(S58)3 2S58 29σd
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