Results for Point Group C20



Symmetric powers of degenerate representation E1
Vibrational overtones


Characters of symmetric powers
Power
To
E 2C20 2C10 2(C20)3 2C5 2C4 2(C10)3 2(C20)7 2(C5)2 2(C20)9 C2
1 2 1.902 1.618 1.176 0.618 0 -0.618 -1.176 -1.618 -1.902 -2
2 3 2.618 1.618 0.382 -0.618 -1 -0.618 0.382 1.618 2.618 3
3 4 3.078 1.000 -0.727 -1.000 0 1.000 0.727 -1.000 -3.078 -4
4 5 3.236 0.000 -1.236 -0.000 1 0.000 -1.236 -0.000 3.236 5
5 6 3.078 -1.000 -0.727 1.000 0 -1.000 0.727 1.000 -3.078 -6
6 7 2.618 -1.618 0.382 0.618 -1 0.618 0.382 -1.618 2.618 7
7 8 1.902 -1.618 1.176 -0.618 0 0.618 -1.176 1.618 -1.902 -8
8 9 1.000 -1.000 1.000 -1.000 1 -1.000 1.000 -1.000 1.000 9
9 10 0.000 -0.000 0.000 -0.000 0 -0.000 0.000 -0.000 0.000 -10
10 11 -1.000 1.000 -1.000 1.000 -1 1.000 -1.000 1.000 -1.000 11
11 12 -1.902 1.618 -1.176 0.618 0 -0.618 1.176 -1.618 1.902 -12
12 13 -2.618 1.618 -0.382 -0.618 1 -0.618 -0.382 1.618 -2.618 13
13 14 -3.078 1.000 0.727 -1.000 0 1.000 -0.727 -1.000 3.078 -14
14 15 -3.236 0.000 1.236 -0.000 -1 0.000 1.236 -0.000 -3.236 15
15 16 -3.078 -1.000 0.727 1.000 0 -1.000 -0.727 1.000 3.078 -16
16 17 -2.618 -1.618 -0.382 0.618 1 0.618 -0.382 -1.618 -2.618 17
17 18 -1.902 -1.618 -1.176 -0.618 0 0.618 1.176 1.618 1.902 -18
18 19 -1.000 -1.000 -1.000 -1.000 -1 -1.000 -1.000 -1.000 -1.000 19
19 20 -0.000 -0.000 -0.000 -0.000 0 -0.000 -0.000 -0.000 -0.000 -20
20 21 1.000 1.000 1.000 1.000 1 1.000 1.000 1.000 1.000 21


Decomposition to irreducible representations
Power
To
A B E1* E2* E3* E4* E5* E6* E7* E8* E9*
1 0 0 1 0 0 0 0 0 0 0 0 E1
2 1 0 0 1 0 0 0 0 0 0 0 A⊕E2
3 0 0 1 0 1 0 0 0 0 0 0 E1⊕E3
4 1 0 0 1 0 1 0 0 0 0 0 A⊕E2⊕E4
5 0 0 1 0 1 0 1 0 0 0 0 E1⊕E3⊕E5
6 1 0 0 1 0 1 0 1 0 0 0 A⊕E2⊕E4⊕E6
7 0 0 1 0 1 0 1 0 1 0 0 E1⊕E3⊕E5⊕E7
8 1 0 0 1 0 1 0 1 0 1 0 A⊕E2⊕E4⊕E6⊕E8
9 0 0 1 0 1 0 1 0 1 0 1 E1⊕E3⊕E5⊕E7⊕E9
10 1 2 0 1 0 1 0 1 0 1 0 A⊕2B⊕E2⊕E4⊕E6⊕E8
11 0 0 1 0 1 0 1 0 1 0 2 E1⊕E3⊕E5⊕E7⊕2E9
12 1 2 0 1 0 1 0 1 0 2 0 A⊕2B⊕E2⊕E4⊕E6⊕2E8
13 0 0 1 0 1 0 1 0 2 0 2 E1⊕E3⊕E5⊕2E7⊕2E9
14 1 2 0 1 0 1 0 2 0 2 0 A⊕2B⊕E2⊕E4⊕2E6⊕2E8
15 0 0 1 0 1 0 2 0 2 0 2 E1⊕E3⊕2E5⊕2E7⊕2E9
16 1 2 0 1 0 2 0 2 0 2 0 A⊕2B⊕E2⊕2E4⊕2E6⊕2E8
17 0 0 1 0 2 0 2 0 2 0 2 E1⊕2E3⊕2E5⊕2E7⊕2E9
18 1 2 0 2 0 2 0 2 0 2 0 A⊕2B⊕2E2⊕2E4⊕2E6⊕2E8
19 0 0 2 0 2 0 2 0 2 0 2 2E1⊕2E3⊕2E5⊕2E7⊕2E9
20 3 2 0 2 0 2 0 2 0 2 0 3A⊕2B⊕2E2⊕2E4⊕2E6⊕2E8



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