C₆ · Neutral gradings
40 neutral gradings · KL, Fourier, Arthur packets
| Ambient orbit | KL block sizes | Arthur parameters | Parameters in packets | Graded orbits | Local systems |
|---|---|---|---|---|---|
| 111111111111 | 1 × 1 | 1 | 1 | 1 | 1 |
| 21111111111 | 2 × 2, 1 × 1 | 2 | 3 | 2 | 3 |
| 2211111111 | 4 × 4, 1 × 1 | 3 | 5 | 3 | 5 |
| 222111111 | 5 × 5, 2 × 2 | 4 | 7 | 4 | 7 |
| 411111111 | 4 × 4, 2 × 2 | 2 | 4 | 4 | 6 |
| 22221111 | 7 × 7, 2 × 2 | 5 | 9 | 5 | 9 |
| 33111111 | 4 × 4 | 3 | 3 | 4 | 4 |
| 42111111 | 10 × 10, 4 × 4, 1 × 1 | 6 | 13 | 8 | 15 |
| 2222211 | 8 × 8, 3 × 3 | 6 | 11 | 6 | 11 |
| 222222 | 10 × 10, 3 × 3 | 7 | 13 | 7 | 13 |
| 3321111 | 8 × 8, 4 × 4 | 6 | 9 | 8 | 12 |
| 4221111 | 16 × 16, 8 × 8, 1 × 1 | 10 | 23 | 12 | 25 |
| 332211 | 16 × 16, 4 × 4 | 9 | 15 | 12 | 20 |
| 6111111 | 8 × 8, 4 × 4 | 2 | 4 | 8 | 12 |
| 422211 | 23 × 23, 10 × 10, 2 × 2 | 14 | 33 | 16 | 35 |
| 33222 | 15 × 15, 6 × 6 | 8 | 14 | 12 | 21 |
| 441111 | 14 × 14, 5 × 5, 1 × 1 | 3 | 8 | 11 | 20 |
| 3333 | 6 × 6 | 3 | 3 | 6 | 6 |
| 42222 | 29 × 29, 14 × 14, 2 × 2 | 18 | 43 | 20 | 45 |
| 621111 | 20 × 20, 8 × 8, 2 × 2 | 4 | 12 | 16 | 30 |
| 43311 | 16 × 16, 8 × 8 | 6 | 12 | 16 | 24 |
| 4332 | 30 × 30, 12 × 12, 3 × 3 | 12 | 26 | 24 | 45 |
| 44211 | 27 × 27, 14 × 14, 2 × 2 | 10 | 29 | 20 | 43 |
| 4422 | 46 × 46, 20 × 20, 4 × 4 | 20 | 56 | 30 | 70 |
| 62211 | 32 × 32, 16 × 16, 2 × 2 | 6 | 20 | 24 | 50 |
| 6222 | 46 × 46, 20 × 20, 4 × 4 | 8 | 28 | 32 | 70 |
| 5511 | 13 × 13 | 2 | 2 | 13 | 13 |
| 81111 | 16 × 16, 8 × 8 | 2 | 4 | 16 | 24 |
| 444 | 32 × 32, 16 × 16, 2 × 2 | 4 | 12 | 24 | 50 |
| 6411 | 36 × 36, 15 × 15, 4 × 4 | 6 | 18 | 29 | 55 |
| 552 | 20 × 20, 10 × 10 | 4 | 6 | 20 | 30 |
| 633 | 24 × 24, 12 × 12 | 4 | 8 | 24 | 36 |
| 8211 | 40 × 40, 16 × 16, 4 × 4 | 4 | 12 | 32 | 60 |
| 642 | 73 × 73, 40 × 40, 8 × 8, 1 × 1 | 18 | 61 | 54 | 122 |
| 66 | 50 × 50, 20 × 20, 5 × 5 | 3 | 8 | 40 | 75 |
| 822 | 64 × 64, 32 × 32, 4 × 4 | 6 | 20 | 48 | 100 |
| 84 | 72 × 72, 30 × 30, 8 × 8 | 4 | 16 | 58 | 110 |
| (10,1,1) | 32 × 32, 16 × 16 | 2 | 4 | 32 | 48 |
| (10,2) | 80 × 80, 32 × 32, 8 × 8 | 4 | 12 | 64 | 120 |
| (12) | 64 × 64, 32 × 32 | 2 | 4 | 64 | 96 |
Counting conventions
Matrix dimensions are listed separately for each block. Parameters in packets counts distinct IC parameters, without multiplicities or repeated membership. Local systems counts orbit–local-system pairs across all exported series. “Not computed” means that the selected export does not contain that result, rather than a count of zero.