Reduction formula for point group D6h



Characters of input representation
E 2C6 (z) 2C3 C2 3C'2 3C''2 i 2S3 2S6 h (xy) 3d 3v
6 0 0 0 -2 0 0 0 0 -6 0 2



Decomposition into Irreducible representations
A1g A2g B1g B2g E1g E2g A1u A2u B1u B2u E1u E2u
0 0 0 1 1 0 0 1 0 0 0 1




Symmetric Powers of Representation


Characters of symmetric powers
Tensor
Order		 E 2C6 (z) 2C3 C2 3C'2 3C''2 i 2S3 2S6 h (xy) 3d 3v
1 6 0 0 0 -2 0 0 0 0 -6 0 2
2 21 0 0 3 5 3 3 0 0 21 3 5
3 56 0 2 0 -8 0 0 -2 0 -56 0 8
4 126 0 0 6 14 6 6 0 0 126 6 14
5 252 0 0 0 -20 0 0 0 0 -252 0 20
6 462 1 3 10 30 10 10 3 1 462 10 30


Decomposition into Irreducible representations
Tensor
Order		 A1g A2g B1g B2g E1g E2g A1u A2u B1u B2u E1u E2u
1 0 0 0 1 1 0 0 1 0 0 0 1
2 4 0 0 0 0 4 0 0 2 1 3 0
3 0 0 3 7 9 0 3 7 0 0 0 9
4 16 6 0 0 0 22 0 0 12 8 20 0
5 0 0 16 26 42 0 16 26 0 0 0 42
6 50 30 0 0 0 78 0 0 43 33 75 0




Antisymmetric Powers of Representation


Characters of antisymmetric powers
Tensor
Order		 E 2C6 (z) 2C3 C2 3C'2 3C''2 i 2S3 2S6 h (xy) 3d 3v
16 0 0 0 -2 0 0 0 0 -6 0 2
215 0 0 -3 -1 -3 -3 0 0 15 -3 -1
320 0 2 0 4 0 0 -2 0 -20 0 -4
4 15 0 0 3 -1 3 3 0 0 15 3 -1
5 6 0 0 0 -2 0 0 0 0 -6 0 2
6 * 1 -1 1 -1 1 -1 -1 1 -1 1 -1 1
* Tensor rank equal tensor order

Decomposition into Irreducible representations
Tensor
Order		 A1g A2g B1g B2g E1g E2g A1u A2u B1u B2u E1u E2u
1 0 0 0 1 1 0 0 1 0 0 0 1
2 0 2 0 0 0 2 0 0 2 1 3 0
3 0 0 3 1 3 0 3 1 0 0 0 3
4 2 1 0 0 0 3 0 0 0 2 2 0
5 0 0 0 1 1 0 0 1 0 0 0 1
6 * 0 0 0 0 0 0 0 0 1 0 0 0
* Tensor rank equal tensor order




Character tables for chemically important point groups Character table for point group D6h Constructor University Bremen
Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement