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23 matroids
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.7.0 | 3 | 7 | 35 | 5040 | ✓ | all | 6 | rational |
| 3.7.1 | 3 | 7 | 34 | 144 | ✓ | all | 5 | rational |
| 3.7.2 | 3 | 7 | 33 | 72 | ✓ | all | 4 | rational |
| 3.7.3 | 3 | 7 | 33 | 16 | ✓ | all | 4 | rational |
| 3.7.4 | 3 | 7 | 32 | 8 | ✓ | all | 3 | rational |
| 3.7.5 | 3 | 7 | 32 | 48 | ✓ | all | 3 | rational |
| 3.7.6 | 3 | 7 | 32 | 6 | ✓ | all | 3 | rational |
| 3.7.7 | 3 | 7 | 31 | 4 | ✓ | all | 2 | rational |
| 3.7.8 | 3 | 7 | 31 | 6 | ✓ | all | 2 | rational |
| 3.7.9 | 3 | 7 | 30 | 12 | ✓ | all | 1 | rational |
| 3.7.10 | 3 | 7 | 31 | 24 | ✓ | all | 2 | rational |
| 3.7.11 | 3 | 7 | 30 | 8 | ✓ | all | 1 | rational |
| 3.7.12 | 3 | 7 | 29 | 24 | ✓ | all but 2 | 0 | rational |
| 3.7.13 | 3 | 7 | 28 | 168 | ✓ | {2} | -1 | empty |
| 3.7.18 | 3 | 7 | 31 | 144 | ✓ | all | 4 | rational |
| 3.7.19 | 3 | 7 | 30 | 144 | ✓ | all | 3 | rational |
| 3.7.20 | 3 | 7 | 30 | 12 | ✓ | all | 2 | rational |
| 3.7.21 | 3 | 7 | 29 | 4 | ✓ | all | 4 | rational |
| 3.7.22 | 3 | 7 | 28 | 6 | ✓ | all | 4 | rational |
| 3.7.23 | 3 | 7 | 27 | 72 | ✓ | all | 3 | rational |
| 3.7.49 | 3 | 7 | 25 | 240 | ✓ | all | 3 | rational |
| 3.7.50 | 3 | 7 | 24 | 48 | ✓ | all | 2 | rational |
| 3.7.85 | 3 | 7 | 15 | 720 | ✓ | all | 2 | rational |