Results for Point Group C19h



Symmetric powers of degenerate representation E'8
Vibrational overtones


Characters of symmetric powers
Power
To		 E C19 (C19)2 (C19)3 (C19)4 (C19)5 (C19)6 (C19)7 (C19)8 (C19)9 (C19)10 (C19)11 (C19)12 (C19)13 (C19)14 (C19)15 (C19)16 (C19)17 (C19)18 σh S19 (S19)21 (S19)3 (S19)23 (S19)5 (S19)25 (S19)7 (S19)27 (S19)9 (S19)29 (S19)11 (S19)31 (S19)13 (S19)33 (S19)15 (S19)35 (S19)17 (S19)37
1 2 -1.759 1.094 -0.165 -0.803 1.578 -1.973 1.892 -1.355 0.491 0.491 -1.355 1.892 -1.973 1.578 -0.803 -0.165 1.094 -1.759 2 -1.759 1.094 -0.165 -0.803 1.578 -1.973 1.892 -1.355 0.491 0.491 -1.355 1.892 -1.973 1.578 -0.803 -0.165 1.094 -1.759
2 3 2.094 0.197 -0.973 -0.355 1.491 2.892 2.578 0.835 -0.759 -0.759 0.835 2.578 2.892 1.491 -0.355 -0.973 0.197 2.094 3 2.094 0.197 -0.973 -0.355 1.491 2.892 2.578 0.835 -0.759 -0.759 0.835 2.578 2.892 1.491 -0.355 -0.973 0.197 2.094
3 4 -1.924 -0.879 0.326 1.088 0.775 -3.732 2.986 0.224 -0.864 -0.864 0.224 2.986 -3.732 0.775 1.088 0.326 -0.879 -1.924 4 -1.924 -0.879 0.326 1.088 0.775 -3.732 2.986 0.224 -0.864 -0.864 0.224 2.986 -3.732 0.775 1.088 0.326 -0.879 -1.924
4 5 1.291 -1.158 0.919 -0.520 -0.268 4.470 3.069 -1.138 0.335 0.335 -1.138 3.069 4.470 -0.268 -0.520 0.919 -1.158 1.291 5 1.291 -1.158 0.919 -0.520 -0.268 4.470 3.069 -1.138 0.335 0.335 -1.138 3.069 4.470 -0.268 -0.520 0.919 -1.158 1.291
5 6 -0.346 -0.388 -0.478 -0.671 -1.198 -5.086 2.820 1.318 1.028 1.028 1.318 2.820 -5.086 -1.198 -0.671 -0.478 -0.388 -0.346 6 -0.346 -0.388 -0.478 -0.671 -1.198 -5.086 2.820 1.318 1.028 1.028 1.318 2.820 -5.086 -1.198 -0.671 -0.478 -0.388 -0.346
6 7 -0.682 0.734 -0.840 1.059 -1.623 5.564 2.266 -0.647 0.170 0.170 -0.647 2.266 5.564 -1.623 1.059 -0.840 0.734 -0.682 7 -0.682 0.734 -0.840 1.059 -1.623 5.564 2.266 -0.647 0.170 0.170 -0.647 2.266 5.564 -1.623 1.059 -0.840 0.734 -0.682
7 8 1.546 1.190 0.616 -0.180 -1.363 -5.890 1.466 -0.441 -0.945 -0.945 -0.441 1.466 -5.890 -1.363 -0.180 0.616 1.190 1.546 8 1.546 1.190 0.616 -0.180 -1.363 -5.890 1.466 -0.441 -0.945 -0.945 -0.441 1.466 -5.890 -1.363 -0.180 0.616 1.190 1.546
8 9 -2.037 0.569 0.738 -0.914 -0.529 6.055 0.507 1.245 -0.634 -0.634 1.245 0.507 6.055 -0.529 -0.914 0.738 0.569 -2.037 9 -2.037 0.569 0.738 -0.914 -0.529 6.055 0.507 1.245 -0.634 -0.634 1.245 0.507 6.055 -0.529 -0.914 0.738 0.569 -2.037
9 10 2.037 -0.569 -0.738 0.914 0.529 -6.055 -0.507 -1.245 0.634 0.634 -1.245 -0.507 -6.055 0.529 0.914 -0.738 -0.569 2.037 10 2.037 -0.569 -0.738 0.914 0.529 -6.055 -0.507 -1.245 0.634 0.634 -1.245 -0.507 -6.055 0.529 0.914 -0.738 -0.569 2.037
10 11 -1.546 -1.190 -0.616 0.180 1.363 5.890 -1.466 0.441 0.945 0.945 0.441 -1.466 5.890 1.363 0.180 -0.616 -1.190 -1.546 11 -1.546 -1.190 -0.616 0.180 1.363 5.890 -1.466 0.441 0.945 0.945 0.441 -1.466 5.890 1.363 0.180 -0.616 -1.190 -1.546
11 12 0.682 -0.734 0.840 -1.059 1.623 -5.564 -2.266 0.647 -0.170 -0.170 0.647 -2.266 -5.564 1.623 -1.059 0.840 -0.734 0.682 12 0.682 -0.734 0.840 -1.059 1.623 -5.564 -2.266 0.647 -0.170 -0.170 0.647 -2.266 -5.564 1.623 -1.059 0.840 -0.734 0.682
12 13 0.346 0.388 0.478 0.671 1.198 5.086 -2.820 -1.318 -1.028 -1.028 -1.318 -2.820 5.086 1.198 0.671 0.478 0.388 0.346 13 0.346 0.388 0.478 0.671 1.198 5.086 -2.820 -1.318 -1.028 -1.028 -1.318 -2.820 5.086 1.198 0.671 0.478 0.388 0.346
13 14 -1.291 1.158 -0.919 0.520 0.268 -4.470 -3.069 1.138 -0.335 -0.335 1.138 -3.069 -4.470 0.268 0.520 -0.919 1.158 -1.291 14 -1.291 1.158 -0.919 0.520 0.268 -4.470 -3.069 1.138 -0.335 -0.335 1.138 -3.069 -4.470 0.268 0.520 -0.919 1.158 -1.291
14 15 1.924 0.879 -0.326 -1.088 -0.775 3.732 -2.986 -0.224 0.864 0.864 -0.224 -2.986 3.732 -0.775 -1.088 -0.326 0.879 1.924 15 1.924 0.879 -0.326 -1.088 -0.775 3.732 -2.986 -0.224 0.864 0.864 -0.224 -2.986 3.732 -0.775 -1.088 -0.326 0.879 1.924
15 16 -2.094 -0.197 0.973 0.355 -1.491 -2.892 -2.578 -0.835 0.759 0.759 -0.835 -2.578 -2.892 -1.491 0.355 0.973 -0.197 -2.094 16 -2.094 -0.197 0.973 0.355 -1.491 -2.892 -2.578 -0.835 0.759 0.759 -0.835 -2.578 -2.892 -1.491 0.355 0.973 -0.197 -2.094
16 17 1.759 -1.094 0.165 0.803 -1.578 1.973 -1.892 1.355 -0.491 -0.491 1.355 -1.892 1.973 -1.578 0.803 0.165 -1.094 1.759 17 1.759 -1.094 0.165 0.803 -1.578 1.973 -1.892 1.355 -0.491 -0.491 1.355 -1.892 1.973 -1.578 0.803 0.165 -1.094 1.759
17 18 -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 18 -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
18 19 -0.000 0.000 -0.000 0.000 -0.000 0.000 0.000 -0.000 0.000 -0.000 0.000 -0.000 -0.000 0.000 -0.000 0.000 0.000 0.000 19 -0.000 0.000 -0.000 0.000 -0.000 0.000 0.000 -0.000 0.000 -0.000 0.000 -0.000 -0.000 0.000 0.000 0.000 -0.000 0.000
19 20 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 20 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
20 21 -1.759 1.094 -0.165 -0.803 1.578 -1.973 1.892 -1.355 0.491 0.491 -1.355 1.892 -1.973 1.578 -0.803 -0.165 1.094 -1.759 21 -1.759 1.094 -0.165 -0.803 1.578 -1.973 1.892 -1.355 0.491 0.491 -1.355 1.892 -1.973 1.578 -0.803 -0.165 1.094 -1.759


Decomposition to irreducible representations
Power
To		 A' E'1* E'2* E'3* E'4* E'5* E'6* E'7* E'8* E'9* A'' E''1* E''2* E''3* E''4* E''5* E''6* E''7* E''8* E''9*
1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 E'8
2 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A'⊕E'3
3 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 E'5⊕E'8
4 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 A'⊕E'3⊕E'6
5 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 E'2⊕E'5⊕E'8
6 1 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 A'⊕E'3⊕E'6⊕E'9
7 0 1 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 E'1⊕E'2⊕E'5⊕E'8
8 1 0 0 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 A'⊕E'3⊕E'6⊕E'7⊕E'9
9 0 1 1 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 E'1⊕E'2⊕E'4⊕E'5⊕E'8
10 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 A'⊕E'3⊕E'4⊕E'6⊕E'7⊕E'9
11 0 1 1 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 E'1⊕E'2⊕E'4⊕E'5⊕E'7⊕E'8
12 1 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 A'⊕E'1⊕E'3⊕E'4⊕E'6⊕E'7⊕E'9
13 0 1 1 0 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 E'1⊕E'2⊕E'4⊕E'5⊕E'7⊕E'8⊕E'9
14 1 1 1 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 A'⊕E'1⊕E'2⊕E'3⊕E'4⊕E'6⊕E'7⊕E'9
15 0 1 1 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 E'1⊕E'2⊕E'4⊕E'5⊕E'6⊕E'7⊕E'8⊕E'9
16 1 1 1 1 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 A'⊕E'1⊕E'2⊕E'3⊕E'4⊕E'5⊕E'6⊕E'7⊕E'9
17 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 E'1⊕E'2⊕E'3⊕E'4⊕E'5⊕E'6⊕E'7⊕E'8⊕E'9
18 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 A'⊕E'1⊕E'2⊕E'3⊕E'4⊕E'5⊕E'6⊕E'7⊕E'8⊕E'9
19 2 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 2A'⊕E'1⊕E'2⊕E'3⊕E'4⊕E'5⊕E'6⊕E'7⊕E'8⊕E'9
20 1 1 1 1 1 1 1 1 2 1 0 0 0 0 0 0 0 0 0 0 A'⊕E'1⊕E'2⊕E'3⊕E'4⊕E'5⊕E'6⊕E'7⊕2E'8⊕E'9


Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement