Point Group D20d

**Characters of symmetric powers**
Power To	E	2S₄₀	2C₂₀	2(S₄₀)³	2C₁₀	2S₈	2(C₂₀)³	2(S₄₀)⁷	2C₅	2(S₄₀)⁹	2C₄	2(S₄₀)¹¹	2(C₁₀)³	2(S₄₀)¹³	2(C₂₀)⁷	2(S₈)³	2(C₅)²	2(S₄₀)¹⁷	2(C₂₀)⁹	2(S₄₀)¹⁹	C₂	20C'₂	20σ_d
1	2	1.975	1.902	1.782	1.618	1.414	1.176	0.908	0.618	0.313	0	-0.313	-0.618	-0.908	-1.176	-1.414	-1.618	-1.782	-1.902	-1.975	-2	0	0
2	3	2.902	2.618	2.176	1.618	1.000	0.382	-0.176	-0.618	-0.902	-1	-0.902	-0.618	-0.176	0.382	1.000	1.618	2.176	2.618	2.902	3	1	1
3	4	3.757	3.078	2.095	1.000	0.000	-0.727	-1.067	-1.000	-0.595	0	0.595	1.000	1.067	0.727	0.000	-1.000	-2.095	-3.078	-3.757	-4	0	0
4	5	4.520	3.236	1.558	0.000	-1.000	-1.236	-0.794	-0.000	0.716	1	0.716	0.000	-0.794	-1.236	-1.000	-0.000	1.558	3.236	4.520	5	1	1
5	6	5.172	3.078	0.681	-1.000	-1.414	-0.727	0.347	1.000	0.819	0	-0.819	-1.000	-0.347	0.727	1.414	1.000	-0.681	-3.078	-5.172	-6	0	0
6	7	5.696	2.618	-0.345	-1.618	-1.000	0.382	1.109	0.618	-0.460	-1	-0.460	0.618	1.109	0.382	-1.000	-1.618	-0.345	2.618	5.696	7	1	1
7	8	6.080	1.902	-1.295	-1.618	-0.000	1.176	0.660	-0.618	-0.963	0	0.963	0.618	-0.660	-1.176	-0.000	1.618	1.295	-1.902	-6.080	-8	0	0
8	9	6.314	1.000	-1.963	-1.000	1.000	1.000	-0.510	-1.000	0.158	1	0.158	-1.000	-0.510	1.000	1.000	-1.000	-1.963	1.000	6.314	9	1	1
9	10	6.392	0.000	-2.203	-0.000	1.414	0.000	-1.122	-0.000	1.012	0	-1.012	-0.000	1.122	0.000	-1.414	-0.000	2.203	-0.000	-6.392	-10	0	0
10	11	6.314	-1.000	-1.963	1.000	1.000	-1.000	-0.510	1.000	0.158	-1	0.158	1.000	-0.510	-1.000	1.000	1.000	-1.963	-1.000	6.314	11	1	1
11	12	6.080	-1.902	-1.295	1.618	0.000	-1.176	0.660	0.618	-0.963	0	0.963	-0.618	-0.660	1.176	0.000	-1.618	1.295	1.902	-6.080	-12	0	0
12	13	5.696	-2.618	-0.345	1.618	-1.000	-0.382	1.109	-0.618	-0.460	1	-0.460	-0.618	1.109	-0.382	-1.000	1.618	-0.345	-2.618	5.696	13	1	1
13	14	5.172	-3.078	0.681	1.000	-1.414	0.727	0.347	-1.000	0.819	0	-0.819	1.000	-0.347	-0.727	1.414	-1.000	-0.681	3.078	-5.172	-14	0	0
14	15	4.520	-3.236	1.558	0.000	-1.000	1.236	-0.794	-0.000	0.716	-1	0.716	0.000	-0.794	1.236	-1.000	-0.000	1.558	-3.236	4.520	15	1	1
15	16	3.757	-3.078	2.095	-1.000	-0.000	0.727	-1.067	1.000	-0.595	0	0.595	-1.000	1.067	-0.727	-0.000	1.000	-2.095	3.078	-3.757	-16	0	0
16	17	2.902	-2.618	2.176	-1.618	1.000	-0.382	-0.176	0.618	-0.902	1	-0.902	0.618	-0.176	-0.382	1.000	-1.618	2.176	-2.618	2.902	17	1	1
17	18	1.975	-1.902	1.782	-1.618	1.414	-1.176	0.908	-0.618	0.313	0	-0.313	0.618	-0.908	1.176	-1.414	1.618	-1.782	1.902	-1.975	-18	0	0
18	19	1.000	-1.000	1.000	-1.000	1.000	-1.000	1.000	-1.000	1.000	-1	1.000	-1.000	1.000	-1.000	1.000	-1.000	1.000	-1.000	1.000	19	1	1
19	20	0.000	-0.000	0.000	-0.000	0.000	-0.000	0.000	-0.000	0.000	0	0.000	-0.000	0.000	-0.000	0.000	-0.000	0.000	0.000	0.000	-20	0	0
20	21	-1.000	1.000	-1.000	1.000	-1.000	1.000	-1.000	1.000	-1.000	1	-1.000	1.000	-1.000	1.000	-1.000	1.000	-1.000	1.000	-1.000	21	1	1

**Decomposition to irreducible representations**
Power To	A₁	B₁	B₂	E₁	E₂	E₃	E₄	E₅	E₆	E₇	E₈	E₉	E₁₀	E₁₁	E₁₂	E₁₃	E₁₄	E₁₅	E₁₆	E₁₇	E₁₈	E₁₉
1	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	E₁
2	1	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	A₁⊕E₂
3	0	0	0	1	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	E₁⊕E₃
4	1	0	0	0	1	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	A₁⊕E₂⊕E₄
5	0	0	0	1	0	1	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	E₁⊕E₃⊕E₅
6	1	0	0	0	1	0	1	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0	A₁⊕E₂⊕E₄⊕E₆
7	0	0	0	1	0	1	0	1	0	1	0	0	0	0	0	0	0	0	0	0	0	0	E₁⊕E₃⊕E₅⊕E₇
8	1	0	0	0	1	0	1	0	1	0	1	0	0	0	0	0	0	0	0	0	0	0	A₁⊕E₂⊕E₄⊕E₆⊕E₈
9	0	0	0	1	0	1	0	1	0	1	0	1	0	0	0	0	0	0	0	0	0	0	E₁⊕E₃⊕E₅⊕E₇⊕E₉
10	1	0	0	0	1	0	1	0	1	0	1	0	1	0	0	0	0	0	0	0	0	0	A₁⊕E₂⊕E₄⊕E₆⊕E₈⊕E₁₀
11	0	0	0	1	0	1	0	1	0	1	0	1	0	1	0	0	0	0	0	0	0	0	E₁⊕E₃⊕E₅⊕E₇⊕E₉⊕E₁₁
12	1	0	0	0	1	0	1	0	1	0	1	0	1	0	1	0	0	0	0	0	0	0	A₁⊕E₂⊕E₄⊕E₆⊕E₈⊕E₁₀⊕E₁₂
13	0	0	0	1	0	1	0	1	0	1	0	1	0	1	0	1	0	0	0	0	0	0	E₁⊕E₃⊕E₅⊕E₇⊕E₉⊕E₁₁⊕E₁₃
14	1	0	0	0	1	0	1	0	1	0	1	0	1	0	1	0	1	0	0	0	0	0	A₁⊕E₂⊕E₄⊕E₆⊕E₈⊕E₁₀⊕E₁₂⊕E₁₄
15	0	0	0	1	0	1	0	1	0	1	0	1	0	1	0	1	0	1	0	0	0	0	E₁⊕E₃⊕E₅⊕E₇⊕E₉⊕E₁₁⊕E₁₃⊕E₁₅
16	1	0	0	0	1	0	1	0	1	0	1	0	1	0	1	0	1	0	1	0	0	0	A₁⊕E₂⊕E₄⊕E₆⊕E₈⊕E₁₀⊕E₁₂⊕E₁₄⊕E₁₆
17	0	0	0	1	0	1	0	1	0	1	0	1	0	1	0	1	0	1	0	1	0	0	E₁⊕E₃⊕E₅⊕E₇⊕E₉⊕E₁₁⊕E₁₃⊕E₁₅⊕E₁₇
18	1	0	0	0	1	0	1	0	1	0	1	0	1	0	1	0	1	0	1	0	1	0	A₁⊕E₂⊕E₄⊕E₆⊕E₈⊕E₁₀⊕E₁₂⊕E₁₄⊕E₁₆⊕E₁₈
19	0	0	0	1	0	1	0	1	0	1	0	1	0	1	0	1	0	1	0	1	0	1	E₁⊕E₃⊕E₅⊕E₇⊕E₉⊕E₁₁⊕E₁₃⊕E₁₅⊕E₁₇⊕E₁₉
20	1	1	1	0	1	0	1	0	1	0	1	0	1	0	1	0	1	0	1	0	1	0	A₁⊕B₁⊕B₂⊕E₂⊕E₄⊕E₆⊕E₈⊕E₁₀⊕E₁₂⊕E₁₄⊕E₁₆⊕E₁₈

Results for Point Group D_20d

Symmetric powers of degenerate representation E₁
Vibrational overtones

Results for Point Group D20d

Symmetric powers of degenerate representation E1Vibrational overtones

Results for Point Group D_20d

Symmetric powers of degenerate representation E₁
Vibrational overtones