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43 matroids
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.7.13 | 3 | 7 | 28 | 168 | ✓ | {2} | -1 | empty |
| 3.7.32 | 3 | 7 | 24 | 8 | ✗ | all | 2 | rational |
| 3.7.36 | 3 | 7 | 21 | 8 | ✗ | all | 1 | rational |
| 3.7.37 | 3 | 7 | 20 | 48 | ✗ | all | 0 | rational |
| 3.7.42 | 3 | 7 | 16 | 24 | ✗ | all | 2 | rational |
| 3.7.57 | 3 | 7 | 20 | 16 | ✗ | all | 0 | rational |
| 3.7.58 | 3 | 7 | 19 | 8 | ✗ | all | 0 | rational |
| 3.7.59 | 3 | 7 | 16 | 16 | ✗ | all | 0 | rational |
| 3.7.64 | 3 | 7 | 18 | 12 | ✗ | all | 2 | rational |
| 3.7.65 | 3 | 7 | 16 | 48 | ✗ | all | 2 | rational |
| 3.7.66 | 3 | 7 | 17 | 24 | ✗ | all | 0 | rational |
| 3.7.67 | 3 | 7 | 15 | 24 | ✗ | all | 3 | rational |
| 3.7.68 | 3 | 7 | 14 | 24 | ✗ | all | 0 | rational |
| 3.7.69 | 3 | 7 | 12 | 48 | ✗ | all | 0 | rational |
| 3.7.71 | 3 | 7 | 13 | 4 | ✗ | all | 0 | rational |
| 3.7.72 | 3 | 7 | 12 | 16 | ✗ | all | 1 | rational |
| 3.7.73 | 3 | 7 | 12 | 16 | ✗ | all | 0 | rational |
| 3.7.74 | 3 | 7 | 10 | 8 | ✗ | all | 2 | rational |
| 3.7.75 | 3 | 7 | 8 | 48 | ✗ | all | 1 | rational |
| 3.7.77 | 3 | 7 | 8 | 16 | ✗ | all | 0 | rational |
| 3.7.78 | 3 | 7 | 13 | 144 | ✗ | all | 0 | rational |
| 3.7.79 | 3 | 7 | 12 | 144 | ✗ | all | 2 | rational |
| 3.7.80 | 3 | 7 | 10 | 36 | ✗ | all | 0 | rational |
| 3.7.81 | 3 | 7 | 9 | 36 | ✗ | all | 0 | rational |
| 3.7.82 | 3 | 7 | 7 | 24 | ✗ | all | 0 | rational |
| 3.7.83 | 3 | 7 | 6 | 24 | ✗ | all | 2 | rational |
| 3.7.84 | 3 | 7 | 4 | 144 | ✗ | all | 1 | rational |
| 3.7.88 | 3 | 7 | 12 | 48 | ✗ | all | 0 | rational |
| 3.7.91 | 3 | 7 | 11 | 12 | ✗ | all | 2 | rational |
| 3.7.92 | 3 | 7 | 9 | 72 | ✗ | all | 2 | rational |
| 3.7.94 | 3 | 7 | 8 | 8 | ✗ | all | 0 | rational |
| 3.7.96 | 3 | 7 | 9 | 48 | ✗ | all | 1 | rational |
| 3.7.97 | 3 | 7 | 8 | 48 | ✗ | all | 1 | rational |
| 3.7.98 | 3 | 7 | 7 | 12 | ✗ | all | 0 | rational |
| 3.7.99 | 3 | 7 | 6 | 12 | ✗ | all | 0 | rational |
| 3.7.100 | 3 | 7 | 5 | 8 | ✗ | all | 0 | rational |
| 3.7.101 | 3 | 7 | 4 | 16 | ✗ | all | 2 | rational |
| 3.7.102 | 3 | 7 | 3 | 36 | ✗ | all | 1 | rational |
| 3.7.103 | 3 | 7 | 5 | 240 | ✗ | all | 1 | rational |
| 3.7.104 | 3 | 7 | 4 | 48 | ✗ | all | 3 | rational |
| 3.7.105 | 3 | 7 | 3 | 24 | ✗ | all | 0 | rational |
| 3.7.106 | 3 | 7 | 2 | 24 | ✗ | all | 3 | rational |
| 3.7.107 | 3 | 7 | 1 | 144 | ✗ | all | 1 | rational |