Point Group D15d

**Characters of symmetric powers**
Power To	E	2C₁₅	2(C₁₅)²	2C₅	2(C₁₅)⁴	2C₃	2(C₅)²	2(C₁₅)⁷	15C'₂	i	2(S₃₀)¹³	2(S₃₀)¹¹	2(S₁₀)³	2(S₃₀)⁷	2S₆	2S₁₀	2S₃₀	15σ_d
1	2	-1.618	0.618	0.618	-1.618	2	-1.618	0.618	0	2	-1.618	0.618	0.618	-1.618	2	-1.618	0.618	0
2	3	1.618	-0.618	-0.618	1.618	3	1.618	-0.618	1	3	1.618	-0.618	-0.618	1.618	3	1.618	-0.618	1
3	4	-1.000	-1.000	-1.000	-1.000	4	-1.000	-1.000	0	4	-1.000	-1.000	-1.000	-1.000	4	-1.000	-1.000	0
4	5	-0.000	0.000	-0.000	-0.000	5	-0.000	0.000	1	5	-0.000	0.000	-0.000	-0.000	5	-0.000	0.000	1
5	6	1.000	1.000	1.000	1.000	6	1.000	1.000	0	6	1.000	1.000	1.000	1.000	6	1.000	1.000	0
6	7	-1.618	0.618	0.618	-1.618	7	-1.618	0.618	1	7	-1.618	0.618	0.618	-1.618	7	-1.618	0.618	1
7	8	1.618	-0.618	-0.618	1.618	8	1.618	-0.618	0	8	1.618	-0.618	-0.618	1.618	8	1.618	-0.618	0
8	9	-1.000	-1.000	-1.000	-1.000	9	-1.000	-1.000	1	9	-1.000	-1.000	-1.000	-1.000	9	-1.000	-1.000	1
9	10	-0.000	0.000	-0.000	-0.000	10	-0.000	0.000	0	10	-0.000	0.000	-0.000	-0.000	10	-0.000	0.000	0
10	11	1.000	1.000	1.000	1.000	11	1.000	1.000	1	11	1.000	1.000	1.000	1.000	11	1.000	1.000	1
11	12	-1.618	0.618	0.618	-1.618	12	-1.618	0.618	0	12	-1.618	0.618	0.618	-1.618	12	-1.618	0.618	0
12	13	1.618	-0.618	-0.618	1.618	13	1.618	-0.618	1	13	1.618	-0.618	-0.618	1.618	13	1.618	-0.618	1
13	14	-1.000	-1.000	-1.000	-1.000	14	-1.000	-1.000	0	14	-1.000	-1.000	-1.000	-1.000	14	-1.000	-1.000	0
14	15	-0.000	0.000	-0.000	-0.000	15	-0.000	0.000	1	15	-0.000	0.000	-0.000	-0.000	15	-0.000	0.000	1
15	16	1.000	1.000	1.000	1.000	16	1.000	1.000	0	16	1.000	1.000	1.000	1.000	16	1.000	1.000	0
16	17	-1.618	0.618	0.618	-1.618	17	-1.618	0.618	1	17	-1.618	0.618	0.618	-1.618	17	-1.618	0.618	1
17	18	1.618	-0.618	-0.618	1.618	18	1.618	-0.618	0	18	1.618	-0.618	-0.618	1.618	18	1.618	-0.618	0
18	19	-1.000	-1.000	-1.000	-1.000	19	-1.000	-1.000	1	19	-1.000	-1.000	-1.000	-1.000	19	-1.000	-1.000	1
19	20	-0.000	0.000	-0.000	-0.000	20	-0.000	0.000	0	20	-0.000	0.000	-0.000	-0.000	20	-0.000	0.000	0
20	21	1.000	1.000	1.000	1.000	21	1.000	1.000	1	21	1.000	1.000	1.000	1.000	21	1.000	1.000	1

**Decomposition to irreducible representations**
Power To	A_1g	A_2g	E_3g	E_6g
1	0	0	0	1	E_6g
2	1	0	1	0	A_1g⊕E_3g
3	0	0	1	1	E_3g⊕E_6g
4	1	0	1	1	A_1g⊕E_3g⊕E_6g
5	1	1	1	1	A_1g⊕A_2g⊕E_3g⊕E_6g
6	1	0	1	2	A_1g⊕E_3g⊕2E_6g
7	1	1	2	1	A_1g⊕A_2g⊕2E_3g⊕E_6g
8	1	0	2	2	A_1g⊕2E_3g⊕2E_6g
9	1	1	2	2	A_1g⊕A_2g⊕2E_3g⊕2E_6g
10	2	1	2	2	2A_1g⊕A_2g⊕2E_3g⊕2E_6g
11	1	1	2	3	A_1g⊕A_2g⊕2E_3g⊕3E_6g
12	2	1	3	2	2A_1g⊕A_2g⊕3E_3g⊕2E_6g
13	1	1	3	3	A_1g⊕A_2g⊕3E_3g⊕3E_6g
14	2	1	3	3	2A_1g⊕A_2g⊕3E_3g⊕3E_6g
15	2	2	3	3	2A_1g⊕2A_2g⊕3E_3g⊕3E_6g
16	2	1	3	4	2A_1g⊕A_2g⊕3E_3g⊕4E_6g
17	2	2	4	3	2A_1g⊕2A_2g⊕4E_3g⊕3E_6g
18	2	1	4	4	2A_1g⊕A_2g⊕4E_3g⊕4E_6g
19	2	2	4	4	2A_1g⊕2A_2g⊕4E_3g⊕4E_6g
20	3	2	4	4	3A_1g⊕2A_2g⊕4E_3g⊕4E_6g

Results for Point Group D_15d

Symmetric powers of degenerate representation E_6g
Vibrational overtones

Results for Point Group D15d

Symmetric powers of degenerate representation E6gVibrational overtones

Results for Point Group D_15d

Symmetric powers of degenerate representation E_6g
Vibrational overtones