Point Group D18d

**Characters of symmetric powers**
Power To	E	2S₃₆	2C₁₈	2S₁₂	2C₉	2(S₃₆)⁵	2C₆	2(S₃₆)⁷	2(C₉)²	2S₄	2(C₁₈)⁵	2(S₃₆)¹¹	2C₃	2(S₃₆)¹³	2(C₁₈)⁷	2(S₁₂)⁵	2(C₉)⁴	2(S₃₆)¹⁷	C₂	18C'₂	18σ_d
1	2	0.347	-1.879	-1.000	1.532	1.532	-1	-1.879	0.347	2	0.347	-1.879	-1	1.532	1.532	-1.000	-1.879	0.347	2	0	0
2	3	-0.879	2.532	0.000	1.347	1.347	0	2.532	-0.879	3	-0.879	2.532	0	1.347	1.347	0.000	2.532	-0.879	3	1	1
3	4	-0.653	-2.879	1.000	0.532	0.532	1	-2.879	-0.653	4	-0.653	-2.879	1	0.532	0.532	1.000	-2.879	-0.653	4	0	0
4	5	0.653	2.879	-1.000	-0.532	-0.532	-1	2.879	0.653	5	0.653	2.879	-1	-0.532	-0.532	-1.000	2.879	0.653	5	1	1
5	6	0.879	-2.532	0.000	-1.347	-1.347	0	-2.532	0.879	6	0.879	-2.532	0	-1.347	-1.347	0.000	-2.532	0.879	6	0	0
6	7	-0.347	1.879	1.000	-1.532	-1.532	1	1.879	-0.347	7	-0.347	1.879	1	-1.532	-1.532	1.000	1.879	-0.347	7	1	1
7	8	-1.000	-1.000	-1.000	-1.000	-1.000	-1	-1.000	-1.000	8	-1.000	-1.000	-1	-1.000	-1.000	-1.000	-1.000	-1.000	8	0	0
8	9	-0.000	-0.000	0.000	0.000	-0.000	0	0.000	0.000	9	-0.000	-0.000	0	-0.000	-0.000	0.000	0.000	-0.000	9	1	1
9	10	1.000	1.000	1.000	1.000	1.000	1	1.000	1.000	10	1.000	1.000	1	1.000	1.000	1.000	1.000	1.000	10	0	0
10	11	0.347	-1.879	-1.000	1.532	1.532	-1	-1.879	0.347	11	0.347	-1.879	-1	1.532	1.532	-1.000	-1.879	0.347	11	1	1
11	12	-0.879	2.532	0.000	1.347	1.347	0	2.532	-0.879	12	-0.879	2.532	0	1.347	1.347	0.000	2.532	-0.879	12	0	0
12	13	-0.653	-2.879	1.000	0.532	0.532	1	-2.879	-0.653	13	-0.653	-2.879	1	0.532	0.532	1.000	-2.879	-0.653	13	1	1
13	14	0.653	2.879	-1.000	-0.532	-0.532	-1	2.879	0.653	14	0.653	2.879	-1	-0.532	-0.532	-1.000	2.879	0.653	14	0	0
14	15	0.879	-2.532	0.000	-1.347	-1.347	0	-2.532	0.879	15	0.879	-2.532	0	-1.347	-1.347	0.000	-2.532	0.879	15	1	1
15	16	-0.347	1.879	1.000	-1.532	-1.532	1	1.879	-0.347	16	-0.347	1.879	1	-1.532	-1.532	1.000	1.879	-0.347	16	0	0
16	17	-1.000	-1.000	-1.000	-1.000	-1.000	-1	-1.000	-1.000	17	-1.000	-1.000	-1	-1.000	-1.000	-1.000	-1.000	-1.000	17	1	1
17	18	-0.000	-0.000	0.000	0.000	-0.000	0	0.000	0.000	18	-0.000	-0.000	0	-0.000	-0.000	0.000	0.000	-0.000	18	0	0
18	19	1.000	1.000	1.000	1.000	1.000	1	1.000	1.000	19	1.000	1.000	1	1.000	1.000	1.000	1.000	1.000	19	1	1
19	20	0.347	-1.879	-1.000	1.532	1.532	-1	-1.879	0.347	20	0.347	-1.879	-1	1.532	1.532	-1.000	-1.879	0.347	20	0	0
20	21	-0.879	2.532	0.000	1.347	1.347	0	2.532	-0.879	21	-0.879	2.532	0	1.347	1.347	0.000	2.532	-0.879	21	1	1

**Decomposition to irreducible representations**
Power To	A₁	A₂	E₄	E₈	E₁₂	E₁₆
1	0	0	0	1	0	0	E₈
2	1	0	0	0	0	1	A₁⊕E₁₆
3	0	0	0	1	1	0	E₈⊕E₁₂
4	1	0	1	0	0	1	A₁⊕E₄⊕E₁₆
5	0	0	1	1	1	0	E₄⊕E₈⊕E₁₂
6	1	0	1	0	1	1	A₁⊕E₄⊕E₁₂⊕E₁₆
7	0	0	1	1	1	1	E₄⊕E₈⊕E₁₂⊕E₁₆
8	1	0	1	1	1	1	A₁⊕E₄⊕E₈⊕E₁₂⊕E₁₆
9	1	1	1	1	1	1	A₁⊕A₂⊕E₄⊕E₈⊕E₁₂⊕E₁₆
10	1	0	1	2	1	1	A₁⊕E₄⊕2E₈⊕E₁₂⊕E₁₆
11	1	1	1	1	1	2	A₁⊕A₂⊕E₄⊕E₈⊕E₁₂⊕2E₁₆
12	1	0	1	2	2	1	A₁⊕E₄⊕2E₈⊕2E₁₂⊕E₁₆
13	1	1	2	1	1	2	A₁⊕A₂⊕2E₄⊕E₈⊕E₁₂⊕2E₁₆
14	1	0	2	2	2	1	A₁⊕2E₄⊕2E₈⊕2E₁₂⊕E₁₆
15	1	1	2	1	2	2	A₁⊕A₂⊕2E₄⊕E₈⊕2E₁₂⊕2E₁₆
16	1	0	2	2	2	2	A₁⊕2E₄⊕2E₈⊕2E₁₂⊕2E₁₆
17	1	1	2	2	2	2	A₁⊕A₂⊕2E₄⊕2E₈⊕2E₁₂⊕2E₁₆
18	2	1	2	2	2	2	2A₁⊕A₂⊕2E₄⊕2E₈⊕2E₁₂⊕2E₁₆
19	1	1	2	3	2	2	A₁⊕A₂⊕2E₄⊕3E₈⊕2E₁₂⊕2E₁₆
20	2	1	2	2	2	3	2A₁⊕A₂⊕2E₄⊕2E₈⊕2E₁₂⊕3E₁₆

Results for Point Group D_18d

Symmetric powers of degenerate representation E₈
Vibrational overtones

Results for Point Group D18d

Symmetric powers of degenerate representation E8Vibrational overtones

Results for Point Group D_18d

Symmetric powers of degenerate representation E₈
Vibrational overtones