Point Group C6

**Characters of symmetric powers**
Power To	E	2C₆	2C₃	C₂
1	2	-1	-1	2
2	3	0	0	3
3	4	1	1	4
4	5	-1	-1	5
5	6	0	0	6
6	7	1	1	7
7	8	-1	-1	8
8	9	0	0	9
9	10	1	1	10
10	11	-1	-1	11
11	12	0	0	12
12	13	1	1	13
13	14	-1	-1	14
14	15	0	0	15
15	16	1	1	16
16	17	-1	-1	17
17	18	0	0	18
18	19	1	1	19
19	20	-1	-1	20
20	21	0	0	21

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

Results for Point Group C₆

Power To	E	2C₆	2C₃	C₂
1	2	-1	-1	2
2	3	0	0	3
3	4	1	1	4
4	5	-1	-1	5
5	6	0	0	6
6	7	1	1	7
7	8	-1	-1	8
8	9	0	0	9
9	10	1	1	10
10	11	-1	-1	11
11	12	0	0	12
12	13	1	1	13
13	14	-1	-1	14
14	15	0	0	15
15	16	1	1	16
16	17	-1	-1	17
17	18	0	0	18
18	19	1	1	19
19	20	-1	-1	20
20	21	0	0	21

Power To	E	2C₆	2C₃	C₂
1	2	-1	-1	2
2	3	0	0	3
3	4	1	1	4
4	5	-1	-1	5
5	6	0	0	6
6	7	1	1	7
7	8	-1	-1	8
8	9	0	0	9
9	10	1	1	10
10	11	-1	-1	11
11	12	0	0	12
12	13	1	1	13
13	14	-1	-1	14
14	15	0	0	15
15	16	1	1	16
16	17	-1	-1	17
17	18	0	0	18
18	19	1	1	19
19	20	-1	-1	20
20	21	0	0	21

Power To	E	2C₆	2C₃	C₂
1	2	-1	-1	2
2	3	0	0	3
3	4	1	1	4
4	5	-1	-1	5
5	6	0	0	6
6	7	1	1	7
7	8	-1	-1	8
8	9	0	0	9
9	10	1	1	10
10	11	-1	-1	11
11	12	0	0	12
12	13	1	1	13
13	14	-1	-1	14
14	15	0	0	15
15	16	1	1	16
16	17	-1	-1	17
17	18	0	0	18
18	19	1	1	19
19	20	-1	-1	20
20	21	0	0	21