Point Group I

**Characters of symmetric powers**
Power To	E	12C₅	12(C₅)²	20C₃	15C₂
1	4	-1.000	-1.000	1	0
2	10	0.000	0.000	1	2
3	20	0.000	0.000	2	0
4	35	0.000	0.000	2	3
5	56	1.000	1.000	2	0
6	84	-1.000	-1.000	3	4
7	120	0.000	0.000	3	0
8	165	0.000	0.000	3	5
9	220	0.000	0.000	4	0
10	286	1.000	1.000	4	6
11	364	-1.000	-1.000	4	0
12	455	0.000	0.000	5	7
13	560	0.000	0.000	5	0
14	680	0.000	0.000	5	8
15	816	1.000	1.000	6	0
16	969	-1.000	-1.000	6	9
17	1.140	0.000	0.000	6	0
18	1.330	0.000	0.000	7	10
19	1.540	0.000	0.000	7	0
20	1.771	1.000	1.000	7	11

**Decomposition to irreducible representations**
Power To	A	T₁	T₂	G	H
1	0	0	0	1	0	G
2	1	0	0	1	1	A⊕G⊕H
3	1	1	1	2	1	A⊕T₁⊕T₂⊕2G⊕H
4	2	1	1	3	3	2A⊕T₁⊕T₂⊕3G⊕3H
5	2	3	3	4	4	2A⊕3T₁⊕3T₂⊕4G⊕4H
6	3	3	3	7	7	3A⊕3T₁⊕3T₂⊕7G⊕7H
7	3	6	6	9	9	3A⊕6T₁⊕6T₂⊕9G⊕9H
8	5	7	7	12	14	5A⊕7T₁⊕7T₂⊕12G⊕14H
9	5	11	11	16	17	5A⊕11T₁⊕11T₂⊕16G⊕17H
10	8	13	13	20	24	8A⊕13T₁⊕13T₂⊕20G⊕24H
11	7	18	18	26	29	7A⊕18T₁⊕18T₂⊕26G⊕29H
12	11	21	21	32	38	11A⊕21T₁⊕21T₂⊕32G⊕38H
13	11	28	28	39	45	11A⊕28T₁⊕28T₂⊕39G⊕45H
14	15	32	32	47	57	15A⊕32T₁⊕32T₂⊕47G⊕57H
15	16	41	41	56	66	16A⊕41T₁⊕41T₂⊕56G⊕66H
16	20	46	46	67	81	20A⊕46T₁⊕46T₂⊕67G⊕81H
17	21	57	57	78	93	21A⊕57T₁⊕57T₂⊕78G⊕93H
18	27	64	64	91	111	27A⊕64T₁⊕64T₂⊕91G⊕111H
19	28	77	77	105	126	28A⊕77T₁⊕77T₂⊕105G⊕126H
20	35	86	86	120	148	35A⊕86T₁⊕86T₂⊕120G⊕148H

Results for Point Group I