Point Group C10

**Characters of symmetric powers**
Power To	E	C₁₀	C₅	(C₁₀)³	(C₅)²	C₂	(C₅)³	(C₁₀)⁷	(C₅)⁴	(C₁₀)⁹
1	2	-0.618	-1.618	1.618	0.618	-2	0.618	1.618	-1.618	-0.618
2	3	-0.618	1.618	1.618	-0.618	3	-0.618	1.618	1.618	-0.618
3	4	1.000	-1.000	1.000	-1.000	-4	-1.000	1.000	-1.000	1.000
4	5	0.000	0.000	-0.000	-0.000	5	0.000	0.000	-0.000	-0.000
5	6	-1.000	1.000	-1.000	1.000	-6	1.000	-1.000	1.000	-1.000
6	7	0.618	-1.618	-1.618	0.618	7	0.618	-1.618	-1.618	0.618
7	8	0.618	1.618	-1.618	-0.618	-8	-0.618	-1.618	1.618	0.618
8	9	-1.000	-1.000	-1.000	-1.000	9	-1.000	-1.000	-1.000	-1.000
9	10	-0.000	0.000	0.000	-0.000	-10	0.000	-0.000	-0.000	0.000
10	11	1.000	1.000	1.000	1.000	11	1.000	1.000	1.000	1.000
11	12	-0.618	-1.618	1.618	0.618	-12	0.618	1.618	-1.618	-0.618
12	13	-0.618	1.618	1.618	-0.618	13	-0.618	1.618	1.618	-0.618
13	14	1.000	-1.000	1.000	-1.000	-14	-1.000	1.000	-1.000	1.000
14	15	0.000	0.000	-0.000	-0.000	15	0.000	0.000	-0.000	-0.000
15	16	-1.000	1.000	-1.000	1.000	-16	1.000	-1.000	1.000	-1.000
16	17	0.618	-1.618	-1.618	0.618	17	0.618	-1.618	-1.618	0.618
17	18	0.618	1.618	-1.618	-0.618	-18	-0.618	-1.618	1.618	0.618
18	19	-1.000	-1.000	-1.000	-1.000	19	-1.000	-1.000	-1.000	-1.000
19	20	-0.000	0.000	0.000	-0.000	-20	0.000	-0.000	-0.000	0.000
20	21	1.000	1.000	1.000	1.000	21	1.000	1.000	1.000	1.000

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

Results for Point Group C₁₀