Characters of symmetric power

Power To	E	S4	C2	(S4)3
1	0	0	0	0
2	0	0	0	0
3	0	0	0	0
4	0	0	0	0
5	0	0	0	0
6	0	0	0	0

Decomposition to irreducible representations
Column for irrep highlighted

Power To	A	B	E*
1	0	0	0
2	0	0	0
3	0	0	0
4	0	0	0
5	0	0	0
6	0	0	0

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Contributions to irrep

pos(X) : Position of irreducible representation (irrep) X in character table of S₄

Subtotal: <Contributions to irrep in subsection> / <number of nonzero irrep combinations in subsection> / <number of irrep combinations in subsection>
Total: <Contributions to irrep > / <number of nonzero irrep combinations in force field> / <number of irrep combinations in force field>

Contributions to irrep for symmetric power to 2

Irrep combinations (i,i) with indices: pos(A) ≤ i ≤ pos(E)
Subtotal: 0 / 0 / 3
Irrep combinations (i,j) with indices: pos(A) ≤ i ≤ j ≤ pos(E)
Subtotal: 0 / 0 / 3
Total: 0 / 0 / 6

Contributions to irrep for symmetric power to 3

Irrep combinations (i,i,i) with indices: pos(A) ≤ i ≤ pos(E)
Subtotal: 0 / 0 / 3
Irrep combinations (i,i,j) (i,j,j) with indices: pos(A) ≤ i ≤ j ≤ pos(E)
Subtotal: 0 / 0 / 6
Irrep combinations (i,j,k) with indices: pos(A) ≤ i ≤ j ≤ k ≤ pos(E)
Subtotal: 0 / 0 / 1
Total: 0 / 0 / 10

Contributions to irrep for symmetric power to 4

Irrep combinations (i,i,i,i) with indices: pos(A) ≤ i ≤ pos(E)
Subtotal: 0 / 0 / 3
Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A) ≤ i ≤ j ≤ pos(E)
Subtotal: 0 / 0 / 6
Irrep combinations (i,i,j,j) with indices: pos(A) ≤ i ≤ j ≤ pos(E)
Subtotal: 0 / 0 / 3
Irrep combinations (i,i,j,k) (i,j,j,k) (i,j,k,k) with indices: pos(A) ≤ i ≤ j ≤ k ≤ pos(E)
Subtotal: 0 / 0 / 3
Irrep combinations (i,j,k,l) with indices: pos(A) ≤ i ≤ j ≤ k ≤ l ≤ pos(E)
Subtotal: 0 / 0 / 0
Total: 0 / 0 / 15

Calculate contributions to

A	B	E

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Max power 4Max power 5Max power 6