Table 35 Weyl group \(D_{4}\), conjugacy class 10, order 6
From: Extending Snow’s algorithm for computations in the finite Weyl groups
\(N^{o}\) in CCL | Element | Level | \(N^{o}\) in Level |
|---|---|---|---|
1 | \(s_{4}s_{3}s_{2}s_{1}\) | 4 | 0 |
2 | \(s_{4}s_{2}s_{3}s_{1}\) | 4 | 2 |
3 | \(s_{2}s_{4}s_{3}s_{1}\) | 4 | 3 |
4 | \(s_{3}s_{2}s_{4}s_{1}\) | 4 | 4 |
5 | \(s_{4}s_{3}s_{1}s_{2}\) | 4 | 9 |
6 | \(s_{4}s_{1}s_{2}s_{3}\) | 4 | 14 |
7 | \(s_{1}s_{2}s_{4}s_{3}\) | 4 | 16 |
8 | \(s_{3}s_{1}s_{2}s_{4}\) | 4 | 20 |
9 | \(s_{2}s_{4}s_{3}s_{2}s_{1}s_{2}\) | 6 | 4 |
10 | \(s_{3}s_{2}s_{4}s_{3}s_{1}s_{2}\) | 6 | 6 |
11 | \(s_{4}s_{2}s_{4}s_{3}s_{1}s_{2}\) | 6 | 7 |
12 | \(s_{2}s_{1}s_{2}s_{4}s_{3}s_{2}\) | 6 | 9 |
13 | \(s_{2}s_{4}s_{3}s_{1}s_{2}s_{3}\) | 6 | 16 |
14 | \(s_{2}s_{4}s_{3}s_{1}s_{2}s_{4}\) | 6 | 27 |
15 | \(s_{3}s_{2}s_{1}s_{2}s_{4}s_{3}s_{2}s_{1}\) | 8 | 0 |
16 | \(s_{4}s_{2}s_{1}s_{2}s_{4}s_{3}s_{2}s_{1}\) | 8 | 1 |
17 | \(s_{2}s_{3}s_{1}s_{2}s_{4}s_{3}s_{2}s_{1}\) | 8 | 2 |
18 | \(s_{2}s_{4}s_{1}s_{2}s_{4}s_{3}s_{2}s_{1}\) | 8 | 4 |
19 | \(s_{4}s_{2}s_{3}s_{1}s_{2}s_{4}s_{3}s_{2}\) | 8 | 8 |
20 | \(s_{3}s_{2}s_{4}s_{1}s_{2}s_{4}s_{3}s_{2}\) | 8 | 10 |
21 | \(s_{3}s_{2}s_{4}s_{3}s_{2}s_{1}s_{2}s_{3}\) | 8 | 12 |
22 | \(s_{4}s_{3}s_{2}s_{4}s_{3}s_{1}s_{2}s_{3}\) | 8 | 14 |
23 | \(s_{3}s_{2}s_{4}s_{3}s_{1}s_{2}s_{4}s_{3}\) | 8 | 17 |
24 | \(s_{4}s_{2}s_{4}s_{3}s_{1}s_{2}s_{4}s_{3}\) | 8 | 18 |
25 | \(s_{4}s_{2}s_{4}s_{3}s_{2}s_{1}s_{2}s_{4}\) | 8 | 21 |
26 | \(s_{4}s_{3}s_{2}s_{4}s_{3}s_{1}s_{2}s_{4}\) | 8 | 22 |
27 | \(s_{4}s_{3}s_{2}s_{3}s_{1}s_{2}s_{4}s_{3}s_{2}s_{1}\) | 10 | 1 |
28 | \(s_{3}s_{2}s_{4}s_{3}s_{1}s_{2}s_{4}s_{3}s_{2}s_{1}\) | 10 | 2 |
29 | \(s_{4}s_{2}s_{4}s_{3}s_{1}s_{2}s_{4}s_{3}s_{2}s_{1}\) | 10 | 3 |
30 | \(s_{4}s_{3}s_{2}s_{4}s_{1}s_{2}s_{4}s_{3}s_{2}s_{1}\) | 10 | 4 |
31 | \(s_{4}s_{3}s_{2}s_{4}s_{3}s_{1}s_{2}s_{4}s_{3}s_{2}\) | 10 | 7 |
32 | \(s_{4}s_{3}s_{2}s_{4}s_{3}s_{2}s_{1}s_{2}s_{4}s_{3}\) | 10 | 8 |