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442 matroids, showing 1–50
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.9.0 | 3 | 9 | 84 | 362880 | ✓ | all | 10 | rational |
| 3.9.1 | 3 | 9 | 83 | 4320 | ✓ | all | 9 | rational |
| 3.9.2 | 3 | 9 | 82 | 432 | ✓ | all | 8 | rational |
| 3.9.3 | 3 | 9 | 81 | 1296 | ✓ | all | 7 | rational |
| 3.9.4 | 3 | 9 | 82 | 192 | ✓ | all | 8 | rational |
| 3.9.5 | 3 | 9 | 81 | 48 | ✓ | all | 7 | rational |
| 3.9.6 | 3 | 9 | 81 | 16 | ✓ | all | 7 | rational |
| 3.9.15 | 3 | 9 | 81 | 36 | ✓ | all | 7 | rational |
| 3.9.163 | 3 | 9 | 77 | 10080 | ✗ | all | 3 | rational |
| 3.9.164 | 3 | 9 | 76 | 288 | ✗ | all | 2 | rational |
| 3.9.177 | 3 | 9 | 56 | 40320 | ✗ | all | 2 | rational |
| 3.9.178 | 3 | 9 | 80 | 2880 | ✓ | all but 2 | 2 | rational |
| 3.9.179 | 3 | 9 | 79 | 288 | ✓ | all but 2 | 1 | rational |
| 3.9.180 | 3 | 9 | 78 | 192 | ✓ | {2} | -1 | rational |
| 3.9.181 | 3 | 9 | 76 | 1152 | ✓ | {2} | -1 | rational |
| 3.9.182 | 3 | 9 | 79 | 72 | ✓ | all | 8 | rational |
| 3.9.183 | 3 | 9 | 78 | 72 | ✓ | all | 7 | rational |
| 3.9.184 | 3 | 9 | 78 | 12 | ✓ | all | 6 | rational |
| 3.9.186 | 3 | 9 | 75 | 72 | ✓ | all | 5 | rational |
| 3.9.187 | 3 | 9 | 78 | 16 | ✓ | all | 5 | rational |
| 3.9.193 | 3 | 9 | 78 | 8 | ✓ | all | 3 | rational |
| 3.9.309 | 3 | 9 | 76 | 144 | ✓ | all | 2 | rational |
| 3.9.310 | 3 | 9 | 75 | 24 | ✓ | all | 1 | rational |
| 3.9.312 | 3 | 9 | 75 | 8 | ✓ | all | 0 | rational |
| 3.9.322 | 3 | 9 | 72 | 48 | ✓ | all but 2 | 1 | rational |
| 3.9.359 | 3 | 9 | 73 | 288 | ✗ | all | 0 | rational |
| 3.9.365 | 3 | 9 | 75 | 480 | ✗ | all | 3 | rational |
| 3.9.366 | 3 | 9 | 74 | 48 | ✗ | all | 2 | rational |
| 3.9.368 | 3 | 9 | 71 | 96 | ✗ | all | 2 | rational |
| 3.9.369 | 3 | 9 | 74 | 24 | ✗ | all | 3 | rational |
| 3.9.397 | 3 | 9 | 71 | 24 | ✗ | all | 3 | rational |
| 3.9.408 | 3 | 9 | 73 | 96 | ✗ | all | 3 | rational |
| 3.9.409 | 3 | 9 | 72 | 96 | ✗ | all | 2 | rational |
| 3.9.410 | 3 | 9 | 72 | 8 | ✗ | all | 3 | rational |
| 3.9.414 | 3 | 9 | 69 | 24 | ✗ | all | 3 | rational |
| 3.9.416 | 3 | 9 | 72 | 8 | ✗ | all | 0 | rational |
| 3.9.459 | 3 | 9 | 69 | 8 | ✗ | all | 3 | rational |
| 3.9.502 | 3 | 9 | 70 | 960 | ✗ | all | 2 | rational |
| 3.9.506 | 3 | 9 | 68 | 48 | ✗ | all | 3 | rational |
| 3.9.511 | 3 | 9 | 66 | 32 | ✗ | all | 2 | rational |
| 3.9.517 | 3 | 9 | 66 | 16 | ✗ | all | 2 | rational |
| 3.9.534 | 3 | 9 | 63 | 288 | ✗ | all | 2 | rational |
| 3.9.540 | 3 | 9 | 55 | 720 | ✗ | all | 1 | rational |
| 3.9.541 | 3 | 9 | 54 | 144 | ✗ | all | 1 | rational |
| 3.9.542 | 3 | 9 | 54 | 48 | ✗ | all | 2 | rational |
| 3.9.543 | 3 | 9 | 53 | 48 | ✗ | all | 1 | rational |
| 3.9.544 | 3 | 9 | 53 | 8 | ✗ | all | 3 | rational |
| 3.9.547 | 3 | 9 | 53 | 12 | ✗ | all | 1 | rational |
| 3.9.571 | 3 | 9 | 65 | 4320 | ✗ | all | 4 | rational |
| 3.9.572 | 3 | 9 | 64 | 216 | ✗ | all | 1 | rational |