Results for Point Group C19h



Symmetric powers of degenerate representation E'9
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 -1.973 1.892 -1.759 1.578 -1.355 1.094 -0.803 0.491 -0.165 -0.165 0.491 -0.803 1.094 -1.355 1.578 -1.759 1.892 -1.973 2 -1.973 1.892 -1.759 1.578 -1.355 1.094 -0.803 0.491 -0.165 -0.165 0.491 -0.803 1.094 -1.355 1.578 -1.759 1.892 -1.973
2 3 2.892 2.578 2.094 1.491 0.835 0.197 -0.355 -0.759 -0.973 -0.973 -0.759 -0.355 0.197 0.835 1.491 2.094 2.578 2.892 3 2.892 2.578 2.094 1.491 0.835 0.197 -0.355 -0.759 -0.973 -0.973 -0.759 -0.355 0.197 0.835 1.491 2.094 2.578 2.892
3 4 -3.732 2.986 -1.924 0.775 0.224 -0.879 1.088 -0.864 0.326 0.326 -0.864 1.088 -0.879 0.224 0.775 -1.924 2.986 -3.732 4 -3.732 2.986 -1.924 0.775 0.224 -0.879 1.088 -0.864 0.326 0.326 -0.864 1.088 -0.879 0.224 0.775 -1.924 2.986 -3.732
4 5 4.470 3.069 1.291 -0.268 -1.138 -1.158 -0.520 0.335 0.919 0.919 0.335 -0.520 -1.158 -1.138 -0.268 1.291 3.069 4.470 5 4.470 3.069 1.291 -0.268 -1.138 -1.158 -0.520 0.335 0.919 0.919 0.335 -0.520 -1.158 -1.138 -0.268 1.291 3.069 4.470
5 6 -5.086 2.820 -0.346 -1.198 1.318 -0.388 -0.671 1.028 -0.478 -0.478 1.028 -0.671 -0.388 1.318 -1.198 -0.346 2.820 -5.086 6 -5.086 2.820 -0.346 -1.198 1.318 -0.388 -0.671 1.028 -0.478 -0.478 1.028 -0.671 -0.388 1.318 -1.198 -0.346 2.820 -5.086
6 7 5.564 2.266 -0.682 -1.623 -0.647 0.734 1.059 0.170 -0.840 -0.840 0.170 1.059 0.734 -0.647 -1.623 -0.682 2.266 5.564 7 5.564 2.266 -0.682 -1.623 -0.647 0.734 1.059 0.170 -0.840 -0.840 0.170 1.059 0.734 -0.647 -1.623 -0.682 2.266 5.564
7 8 -5.890 1.466 1.546 -1.363 -0.441 1.190 -0.180 -0.945 0.616 0.616 -0.945 -0.180 1.190 -0.441 -1.363 1.546 1.466 -5.890 8 -5.890 1.466 1.546 -1.363 -0.441 1.190 -0.180 -0.945 0.616 0.616 -0.945 -0.180 1.190 -0.441 -1.363 1.546 1.466 -5.890
8 9 6.055 0.507 -2.037 -0.529 1.245 0.569 -0.914 -0.634 0.738 0.738 -0.634 -0.914 0.569 1.245 -0.529 -2.037 0.507 6.055 9 6.055 0.507 -2.037 -0.529 1.245 0.569 -0.914 -0.634 0.738 0.738 -0.634 -0.914 0.569 1.245 -0.529 -2.037 0.507 6.055
9 10 -6.055 -0.507 2.037 0.529 -1.245 -0.569 0.914 0.634 -0.738 -0.738 0.634 0.914 -0.569 -1.245 0.529 2.037 -0.507 -6.055 10 -6.055 -0.507 2.037 0.529 -1.245 -0.569 0.914 0.634 -0.738 -0.738 0.634 0.914 -0.569 -1.245 0.529 2.037 -0.507 -6.055
10 11 5.890 -1.466 -1.546 1.363 0.441 -1.190 0.180 0.945 -0.616 -0.616 0.945 0.180 -1.190 0.441 1.363 -1.546 -1.466 5.890 11 5.890 -1.466 -1.546 1.363 0.441 -1.190 0.180 0.945 -0.616 -0.616 0.945 0.180 -1.190 0.441 1.363 -1.546 -1.466 5.890
11 12 -5.564 -2.266 0.682 1.623 0.647 -0.734 -1.059 -0.170 0.840 0.840 -0.170 -1.059 -0.734 0.647 1.623 0.682 -2.266 -5.564 12 -5.564 -2.266 0.682 1.623 0.647 -0.734 -1.059 -0.170 0.840 0.840 -0.170 -1.059 -0.734 0.647 1.623 0.682 -2.266 -5.564
12 13 5.086 -2.820 0.346 1.198 -1.318 0.388 0.671 -1.028 0.478 0.478 -1.028 0.671 0.388 -1.318 1.198 0.346 -2.820 5.086 13 5.086 -2.820 0.346 1.198 -1.318 0.388 0.671 -1.028 0.478 0.478 -1.028 0.671 0.388 -1.318 1.198 0.346 -2.820 5.086
13 14 -4.470 -3.069 -1.291 0.268 1.138 1.158 0.520 -0.335 -0.919 -0.919 -0.335 0.520 1.158 1.138 0.268 -1.291 -3.069 -4.470 14 -4.470 -3.069 -1.291 0.268 1.138 1.158 0.520 -0.335 -0.919 -0.919 -0.335 0.520 1.158 1.138 0.268 -1.291 -3.069 -4.470
14 15 3.732 -2.986 1.924 -0.775 -0.224 0.879 -1.088 0.864 -0.326 -0.326 0.864 -1.088 0.879 -0.224 -0.775 1.924 -2.986 3.732 15 3.732 -2.986 1.924 -0.775 -0.224 0.879 -1.088 0.864 -0.326 -0.326 0.864 -1.088 0.879 -0.224 -0.775 1.924 -2.986 3.732
15 16 -2.892 -2.578 -2.094 -1.491 -0.835 -0.197 0.355 0.759 0.973 0.973 0.759 0.355 -0.197 -0.835 -1.491 -2.094 -2.578 -2.892 16 -2.892 -2.578 -2.094 -1.491 -0.835 -0.197 0.355 0.759 0.973 0.973 0.759 0.355 -0.197 -0.835 -1.491 -2.094 -2.578 -2.892
16 17 1.973 -1.892 1.759 -1.578 1.355 -1.094 0.803 -0.491 0.165 0.165 -0.491 0.803 -1.094 1.355 -1.578 1.759 -1.892 1.973 17 1.973 -1.892 1.759 -1.578 1.355 -1.094 0.803 -0.491 0.165 0.165 -0.491 0.803 -1.094 1.355 -1.578 1.759 -1.892 1.973
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 -1.973 1.892 -1.759 1.578 -1.355 1.094 -0.803 0.491 -0.165 -0.165 0.491 -0.803 1.094 -1.355 1.578 -1.759 1.892 -1.973 21 -1.973 1.892 -1.759 1.578 -1.355 1.094 -0.803 0.491 -0.165 -0.165 0.491 -0.803 1.094 -1.355 1.578 -1.759 1.892 -1.973


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 0 1 0 0 0 0 0 0 0 0 0 0 E'9
2 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A'⊕E'1
3 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 E'8⊕E'9
4 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A'⊕E'1⊕E'2
5 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 E'7⊕E'8⊕E'9
6 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A'⊕E'1⊕E'2⊕E'3
7 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 E'6⊕E'7⊕E'8⊕E'9
8 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A'⊕E'1⊕E'2⊕E'3⊕E'4
9 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 E'5⊕E'6⊕E'7⊕E'8⊕E'9
10 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A'⊕E'1⊕E'2⊕E'3⊕E'4⊕E'5
11 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 E'4⊕E'5⊕E'6⊕E'7⊕E'8⊕E'9
12 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 A'⊕E'1⊕E'2⊕E'3⊕E'4⊕E'5⊕E'6
13 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 E'3⊕E'4⊕E'5⊕E'6⊕E'7⊕E'8⊕E'9
14 1 1 1 1 1 1 1 1 0 0 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
15 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 E'2⊕E'3⊕E'4⊕E'5⊕E'6⊕E'7⊕E'8⊕E'9
16 1 1 1 1 1 1 1 1 1 0 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
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 1 2 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⊕2E'9



Last update January, 3rd 2020 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement