Point Group T

**Characters of symmetric powers**
Power To	E	8C₃	3C₂
1	3	0	-1
2	6	0	2
3	10	1	-2
4	15	0	3
5	21	0	-3
6	28	1	4
7	36	0	-4
8	45	0	5
9	55	1	-5
10	66	0	6
11	78	0	-6
12	91	1	7
13	105	0	-7
14	120	0	8
15	136	1	-8
16	153	0	9
17	171	0	-9
18	190	1	10
19	210	0	-10
20	231	0	11

**Decomposition to irreducible representations**
Power To	A	E*	T
1	0	0	1	T
2	1	1	1	A⊕E⊕T
3	1	0	3	A⊕3T
4	2	2	3	2A⊕2E⊕3T
5	1	1	6	A⊕E⊕6T
6	4	3	6	4A⊕3E⊕6T
7	2	2	10	2A⊕2E⊕10T
8	5	5	10	5A⊕5E⊕10T
9	4	3	15	4A⊕3E⊕15T
10	7	7	15	7A⊕7E⊕15T
11	5	5	21	5A⊕5E⊕21T
12	10	9	21	10A⊕9E⊕21T
13	7	7	28	7A⊕7E⊕28T
14	12	12	28	12A⊕12E⊕28T
15	10	9	36	10A⊕9E⊕36T
16	15	15	36	15A⊕15E⊕36T
17	12	12	45	12A⊕12E⊕45T
18	19	18	45	19A⊕18E⊕45T
19	15	15	55	15A⊕15E⊕55T
20	22	22	55	22A⊕22E⊕55T

Results for Point Group T

Power To	E	8C₃	3C₂
1	3	0	-1
2	6	0	2
3	10	1	-2
4	15	0	3
5	21	0	-3
6	28	1	4
7	36	0	-4
8	45	0	5
9	55	1	-5
10	66	0	6
11	78	0	-6
12	91	1	7
13	105	0	-7
14	120	0	8
15	136	1	-8
16	153	0	9
17	171	0	-9
18	190	1	10
19	210	0	-10
20	231	0	11

Power To	E	8C₃	3C₂
1	3	0	-1
2	6	0	2
3	10	1	-2
4	15	0	3
5	21	0	-3
6	28	1	4
7	36	0	-4
8	45	0	5
9	55	1	-5
10	66	0	6
11	78	0	-6
12	91	1	7
13	105	0	-7
14	120	0	8
15	136	1	-8
16	153	0	9
17	171	0	-9
18	190	1	10
19	210	0	-10
20	231	0	11

Power To	E	8C₃	3C₂
1	3	0	-1
2	6	0	2
3	10	1	-2
4	15	0	3
5	21	0	-3
6	28	1	4
7	36	0	-4
8	45	0	5
9	55	1	-5
10	66	0	6
11	78	0	-6
12	91	1	7
13	105	0	-7
14	120	0	8
15	136	1	-8
16	153	0	9
17	171	0	-9
18	190	1	10
19	210	0	-10
20	231	0	11