Point Group C20v

**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	10σ_v	10σ_d
1	2	0.618	-1.618	-1.618	0.618	2	0.618	-1.618	-1.618	0.618	2	0	0
2	3	-0.618	1.618	1.618	-0.618	3	-0.618	1.618	1.618	-0.618	3	1	1
3	4	-1.000	-1.000	-1.000	-1.000	4	-1.000	-1.000	-1.000	-1.000	4	0	0
4	5	-0.000	-0.000	0.000	0.000	5	-0.000	-0.000	0.000	0.000	5	1	1
5	6	1.000	1.000	1.000	1.000	6	1.000	1.000	1.000	1.000	6	0	0
6	7	0.618	-1.618	-1.618	0.618	7	0.618	-1.618	-1.618	0.618	7	1	1
7	8	-0.618	1.618	1.618	-0.618	8	-0.618	1.618	1.618	-0.618	8	0	0
8	9	-1.000	-1.000	-1.000	-1.000	9	-1.000	-1.000	-1.000	-1.000	9	1	1
9	10	-0.000	-0.000	0.000	0.000	10	-0.000	-0.000	0.000	0.000	10	0	0
10	11	1.000	1.000	1.000	1.000	11	1.000	1.000	1.000	1.000	11	1	1
11	12	0.618	-1.618	-1.618	0.618	12	0.618	-1.618	-1.618	0.618	12	0	0
12	13	-0.618	1.618	1.618	-0.618	13	-0.618	1.618	1.618	-0.618	13	1	1
13	14	-1.000	-1.000	-1.000	-1.000	14	-1.000	-1.000	-1.000	-1.000	14	0	0
14	15	-0.000	-0.000	0.000	0.000	15	-0.000	-0.000	0.000	0.000	15	1	1
15	16	1.000	1.000	1.000	1.000	16	1.000	1.000	1.000	1.000	16	0	0
16	17	0.618	-1.618	-1.618	0.618	17	0.618	-1.618	-1.618	0.618	17	1	1
17	18	-0.618	1.618	1.618	-0.618	18	-0.618	1.618	1.618	-0.618	18	0	0
18	19	-1.000	-1.000	-1.000	-1.000	19	-1.000	-1.000	-1.000	-1.000	19	1	1
19	20	-0.000	-0.000	0.000	0.000	20	-0.000	-0.000	0.000	0.000	20	0	0
20	21	1.000	1.000	1.000	1.000	21	1.000	1.000	1.000	1.000	21	1	1

**Decomposition to irreducible representations**
Power To	A₁	A₂	E₄	E₈
1	0	0	1	0	E₄
2	1	0	0	1	A₁⊕E₈
3	0	0	1	1	E₄⊕E₈
4	1	0	1	1	A₁⊕E₄⊕E₈
5	1	1	1	1	A₁⊕A₂⊕E₄⊕E₈
6	1	0	2	1	A₁⊕2E₄⊕E₈
7	1	1	1	2	A₁⊕A₂⊕E₄⊕2E₈
8	1	0	2	2	A₁⊕2E₄⊕2E₈
9	1	1	2	2	A₁⊕A₂⊕2E₄⊕2E₈
10	2	1	2	2	2A₁⊕A₂⊕2E₄⊕2E₈
11	1	1	3	2	A₁⊕A₂⊕3E₄⊕2E₈
12	2	1	2	3	2A₁⊕A₂⊕2E₄⊕3E₈
13	1	1	3	3	A₁⊕A₂⊕3E₄⊕3E₈
14	2	1	3	3	2A₁⊕A₂⊕3E₄⊕3E₈
15	2	2	3	3	2A₁⊕2A₂⊕3E₄⊕3E₈
16	2	1	4	3	2A₁⊕A₂⊕4E₄⊕3E₈
17	2	2	3	4	2A₁⊕2A₂⊕3E₄⊕4E₈
18	2	1	4	4	2A₁⊕A₂⊕4E₄⊕4E₈
19	2	2	4	4	2A₁⊕2A₂⊕4E₄⊕4E₈
20	3	2	4	4	3A₁⊕2A₂⊕4E₄⊕4E₈

Results for Point Group C_20v