Results for Point Group C19h



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


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


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