by Dimitri Leemans and Bernardo Rodrigues
This atlas contains all primitive geometries of rank two obtained from the 12 smallest sporadic simple groups, using the algorithm described in the paper "On primitive geometries of rank two".
By clicking on a link in the tables below, you'll download a Magma file containing the geometries for the selected group.
| G | Order of G | Number of geometries |
|---|---|---|
| M11 | 7920 | 37 |
| M12 | 95040 | 166 |
| M22 | 443530 | 81 |
| M23 | 10200960 | 170 |
| M24 | 244823040 | 5074 |
| J1 | 175560 | 669 |
| J2 | 604800 | 334 |
| J3 | 50232960 | 546 |
| HS | 44352000 | 339 |
| McL | 898128000 | 443 |
| He | 4030387200 | 4074 |
| Ru | 145926144000 | 1511 |