Point Group S30

**Characters of symmetric powers**
Power To	E	C₁₅	(C₁₅)²	C₅	(C₁₅)⁴	C₃	(C₅)²	(C₁₅)⁷	(C₁₅)⁸	(C₅)³	(C₃)²	(C₁₅)¹¹	(C₅)⁴	(C₁₅)¹³	(C₁₅)¹⁴	i	(S₃₀)¹⁷	(S₃₀)¹⁹	(S₁₀)⁷	(S₃₀)²³	(S₆)⁵	(S₁₀)⁹	(S₃₀)²⁹	S₃₀	S₁₀	S₆	(S₃₀)⁷	(S₁₀)³	(S₃₀)¹¹	(S₃₀)¹³
1	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000
2	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000
3	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000
4	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000
5	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000
6	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000
7	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000
8	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000
9	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000
10	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000
11	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000
12	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000
13	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000
14	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000
15	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000
16	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000
17	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000
18	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000
19	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000
20	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000

**Decomposition to irreducible representations**
Power To	A_g	E_1g*	E_2g*	E_3g*	E_4g*	E_5g*	E_6g*	E_7g*	A_u	E_1u*	E_2u*	E_3u*	E_4u*	E_5u*	E_6u*	E_7u*
1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
3	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
4	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
5	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
6	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
7	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
8	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
9	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
10	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
11	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
12	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
13	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
14	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
15	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
16	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
17	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
18	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
19	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
20	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0

Antisymmetric Powers of Representation

**Characters of antisymmetric powers**
Power To	E	C₁₅	(C₁₅)²	C₅	(C₁₅)⁴	C₃	(C₅)²	(C₁₅)⁷	(C₁₅)⁸	(C₅)³	(C₃)²	(C₁₅)¹¹	(C₅)⁴	(C₁₅)¹³	(C₁₅)¹⁴	i	(S₃₀)¹⁷	(S₃₀)¹⁹	(S₁₀)⁷	(S₃₀)²³	(S₆)⁵	(S₁₀)⁹	(S₃₀)²⁹	S₃₀	S₁₀	S₆	(S₃₀)⁷	(S₁₀)³	(S₃₀)¹¹	(S₃₀)¹³
≥1	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000	0	0.000	0.000	0.000	0.000

**Decomposition to irreducible representations**
Power To	A_g	E_1g*	E_2g*	E_3g*	E_4g*	E_5g*	E_6g*	E_7g*	A_u	E_1u*	E_2u*	E_3u*	E_4u*	E_5u*	E_6u*	E_7u*
≥1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0

Results for Point Group S₃₀

Symmetric Powers of Representation

Antisymmetric Powers of Representation

Power To	A_g	E_1g*	E_2g*	E_3g*	E_4g*	E_5g*	E_6g*	E_7g*	A_u	E_1u*	E_2u*	E_3u*	E_4u*	E_5u*	E_6u*	E_7u*
1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
3	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
4	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
5	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
6	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
7	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
8	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
9	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
10	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
11	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
12	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
13	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
14	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
15	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
16	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
17	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
18	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
19	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
20	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0

Power To	A_g	E_1g*	E_2g*	E_3g*	E_4g*	E_5g*	E_6g*	E_7g*	A_u	E_1u*	E_2u*	E_3u*	E_4u*	E_5u*	E_6u*	E_7u*
1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
3	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
4	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
5	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
6	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
7	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
8	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
9	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
10	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
11	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
12	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
13	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
14	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
15	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
16	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
17	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
18	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
19	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
20	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0

Results for Point Group S30

Symmetric Powers of Representation

Antisymmetric Powers of Representation

Results for Point Group S₃₀

Power To	A_g	E_1g*	E_2g*	E_3g*	E_4g*	E_5g*	E_6g*	E_7g*	A_u	E_1u*	E_2u*	E_3u*	E_4u*	E_5u*	E_6u*	E_7u*
1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
2	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
3	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
4	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
5	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
6	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
7	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
8	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
9	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
10	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
11	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
12	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
13	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
14	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
15	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
16	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
17	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
18	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
19	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
20	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0