Results for Point Group C19h



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


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 0 0 0 0 0 0 1 0 0 0 0 E''5
2 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 A'⊕E'9
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 E''4⊕E''5
4 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 A'⊕E'1⊕E'9
5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 E''4⊕E''5⊕E''6
6 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 A'⊕E'1⊕E'8⊕E'9
7 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 E''3⊕E''4⊕E''5⊕E''6
8 1 1 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 A'⊕E'1⊕E'2⊕E'8⊕E'9
9 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 E''3⊕E''4⊕E''5⊕E''6⊕E''7
10 1 1 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 A'⊕E'1⊕E'2⊕E'7⊕E'8⊕E'9
11 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 E''2⊕E''3⊕E''4⊕E''5⊕E''6⊕E''7
12 1 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 A'⊕E'1⊕E'2⊕E'3⊕E'7⊕E'8⊕E'9
13 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 E''2⊕E''3⊕E''4⊕E''5⊕E''6⊕E''7⊕E''8
14 1 1 1 1 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 A'⊕E'1⊕E'2⊕E'3⊕E'6⊕E'7⊕E'8⊕E'9
15 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 E''1⊕E''2⊕E''3⊕E''4⊕E''5⊕E''6⊕E''7⊕E''8
16 1 1 1 1 1 0 1 1 1 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'8⊕E'9
17 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 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 0 0 0 0 0 0 0 0 0 0 2 1 1 1 1 1 1 1 1 1 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 2 1 1 1 1 0 0 0 0 0 0 0 0 0 0 A'⊕E'1⊕E'2⊕E'3⊕E'4⊕2E'5⊕E'6⊕E'7⊕E'8⊕E'9


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