On this page, we record details of the work to be done on the ATLAS. Use the links on the right to select an area of interest.
- Groups with porting problems.
- Failing matrix representations
- Failing permutation representations
- Failing presentations
- Failing subgroup programs
- Problematic representations
Classical groups
| Lead group | Group | Gens | Pres | Check | Find | Perm rep | Matrix rep | Conj cl | Maxes |
|---|---|---|---|---|---|---|---|---|---|
| S4(2)' | A6 | 1 | 1 | 1 | 0 | 5 | 23 | 7/7 | 5/5 |
| 2.A6 | 1 | 0 | 0 | 0 | 4 | 14 | 0/0 | 0/0 | |
| 3.A6 | 1 | 0 | 0 | 0 | 4 | 16 | 0/0 | 0/0 | |
| 6.A6 | 1 | 0 | 0 | 0 | 2 | 6 | 0/0 | 0/0 | |
| S6 | 1 | 1 | 0 | 0 | 5 | 0 | 12/11 | 6/6 | |
| 2.S6 | 1 | 0 | 0 | 0 | 3 | 0 | 0/0 | 0/0 | |
| 3.S6 | 1 | 0 | 0 | 0 | 4 | 0 | 0/0 | 0/0 | |
| 6.S6 | 1 | 0 | 0 | 0 | 1 | 0 | 0/0 | 0/0 | |
| PGL2(9) | 1 | 1 | 0 | 0 | 1 | 0 | 13/13 | 0/0 | |
| 2.PGL2(9) | 1 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| 3.PGL2(9) | 1 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| 6.PGL2(9) | 1 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| M10 | 1 | 1 | 0 | 0 | 1 | 0 | 8/8 | 0/0 | |
| 3.M10 | 1 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| Aut(A6) | 1 | 1 | 0 | 0 | 1 | 0 | 13/13 | 0/0 | |
| 3.Aut(A6) | 1 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| S4(3) | U4(2) | 1 | 1 | 1 | 0 | 5 | 33 | 20/20 | 0/0 |
| 2.U4(2) | 1 | 0 | 0 | 0 | 2 | 12 | 0/0 | 0/0 | |
| U4(2):2 | 1 | 0 | 0 | 0 | 5 | 9 | 25/25 | 0/0 | |
| 2.U4(2):2 | 1 | 0 | 0 | 0 | 1 | 1 | 0/0 | 0/0 | |
| S4(4) | S4(4) | 1 | 0 | 1 | 0 | 2 | 28 | 0/0 | 7/7 |
| S4(4):2 | 1 | 0 | 0 | 0 | 0 | 1 | 0/0 | 0/0 | |
| S4(4):4 | 1 | 0 | 0 | 0 | 1 | 1 | 0/0 | 0/0 | |
| S4(5) | S4(5) | 1 | 0 | 1 | 0 | 4 | 17 | 0/0 | 8/8 |
| 2.S4(5) | 1 | 0 | 0 | 0 | 1 | 1 | 0/0 | 0/0 | |
| S4(5):2 | 1 | 0 | 0 | 0 | 0 | 7 | 0/0 | 0/0 | |
| 2.S4(5):2 | 1 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| 2.S4(5).2 (isoclinic) | 1 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| S4(7) | S4(7) | 1 | 0 | 1 | 0 | 4 | 7 | 0/0 | 0/0 |
| 2.S4(7) | 1 | 0 | 0 | 0 | 0 | 1 | 0/0 | 0/0 | |
| S4(7):2 | 1 | 0 | 0 | 0 | 2 | 1 | 0/0 | 0/0 | |
| 2.S4(7):2 | 1 | 0 | 0 | 0 | 0 | 1 | 0/0 | 0/0 | |
| S4(9) | 2.S4(9) | 0 | 0 | 0 | 0 | 0 | 1 | 0/0 | 0/0 |
| S4(9) | 1 | 0 | 1 | 0 | 3 | 2 | 0/0 | 0/0 | |
| S4(11) | S4(11) | 1 | 0 | 0 | 0 | 3 | 3 | 0/0 | 0/0 |
| 2.S4(11) | 0 | 0 | 0 | 0 | 0 | 1 | 0/0 | 0/0 | |
| S4(11):2 | 0 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| 2.S4(11):2 | 0 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| S4(13) | S4(13) | 1 | 0 | 0 | 0 | 3 | 1 | 0/0 | 0/0 |
| 2.S4(13) | 0 | 0 | 0 | 0 | 0 | 1 | 0/0 | 0/0 | |
| S4(13):2 | 0 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| 2.S4(13):2 | 0 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| S4(17) | S4(17) | 1 | 0 | 0 | 0 | 3 | 1 | 0/0 | 0/0 |
| 2.S4(17) | 0 | 0 | 0 | 0 | 0 | 1 | 0/0 | 0/0 | |
| S4(17):2 | 0 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| 2.S4(17):2 | 0 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| S4(19) | S4(19) | 1 | 0 | 0 | 0 | 3 | 1 | 0/0 | 0/0 |
| 2.S4(19) | 0 | 0 | 0 | 0 | 0 | 1 | 0/0 | 0/0 | |
| S4(19):2 | 0 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| 2.S4(19):2 | 0 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| S6(2) | S6(2) | 1 | 1 | 1 | 0 | 15 | 45 | 30/30 | 8/8 |
| 2.S6(2) | 1 | 1 | 0 | 0 | 5 | 7 | 0/0 | 0/0 | |
| S6(3) | S6(3) | 1 | 0 | 0 | 0 | 4 | 12 | 0/0 | 10/11 |
| 2.S6(3) | 1 | 0 | 0 | 0 | 0 | 1 | 0/0 | 0/0 | |
| S6(3):2 | 1 | 0 | 0 | 0 | 4 | 2 | 0/0 | 0/9 | |
| 2.S6(3).2 | 1 | 0 | 0 | 0 | 1 | 1 | 0/0 | 0/0 | |
| 2.S6(3).2 (isoclinic) | 1 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| S6(5) | S6(5) | 1 | 0 | 0 | 0 | 1 | 2 | 0/0 | 0/0 |
| 2.S6(5) | 1 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| S6(5):2 | 0 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| 2.S6(5):2 | 0 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| S8(2) | S8(2) | 1 | 0 | 0 | 0 | 7 | 17 | 0/0 | 0/0 |
| S8(3) | S8(3) | 1 | 0 | 0 | 0 | 1 | 2 | 0/0 | 0/0 |
| 2.S8(3) | 1 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| S8(3):2 | 0 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| 2.S8(3):2 | 0 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| S10(2) | S10(2) | 1 | 1 | 0 | 0 | 5 | 14 | 0/0 | 0/0 |
| U3(3) | U3(3) | 1 | 1 | 0 | 0 | 4 | 34 | 0/0 | 0/0 |
| U3(3):2 | 1 | 1 | 0 | 0 | 1 | 8 | 0/0 | 0/0 | |
| U3(4) | U3(4) | 2 | 1 | 0 | 0 | 4 | 62 | 0/0 | 4/4 |
| U3(4):2 | 1 | 1 | 0 | 0 | 4 | 0 | 0/0 | 5/5 | |
| U3(4):4 | 1 | 1 | 0 | 0 | 4 | 23 | 0/0 | 5/5 | |
| U3(5) | U3(5) | 1 | 1 | 0 | 0 | 1 | 11 | 0/0 | 0/8 |
| 3.U3(5) | 1 | 0 | 0 | 0 | 0 | 1 | 0/0 | 0/0 | |
| U3(5):2 | 1 | 1 | 0 | 0 | 5 | 28 | 0/0 | 7/6 | |
| 3.U3(5):2 | 1 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| U3(5):3 | 1 | 1 | 0 | 0 | 0 | 0 | 0/0 | 0/6 | |
| 3.U3(5).3 | 1 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| U3(5):S3 | 1 | 1 | 0 | 0 | 0 | 0 | 0/0 | 0/7 | |
| 3.U3(5).S3 | 1 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| U3(7) | U3(7) | 1 | 1 | 0 | 0 | 9 | 20 | 0/0 | 5/5 |
| U3(7).2 | 1 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| U3(8) | U3(8) | 1 | 1 | 0 | 0 | 2 | 7 | 0/0 | 0/0 |
| 3.U3(8) | 1 | 0 | 0 | 0 | 2 | 1 | 0/0 | 0/0 | |
| U3(8):2 | 1 | 0 | 0 | 0 | 2 | 0 | 0/0 | 0/0 | |
| 3.U3(8):2 | 1 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| U3(8):31 | 1 | 0 | 0 | 0 | 2 | 0 | 0/0 | 0/0 | |
| 3.U3(8):31 | 1 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| U3(8):6 | 1 | 0 | 0 | 0 | 2 | 9 | 0/0 | 0/0 | |
| 3.U3(8):6 | 0 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| U3(8):32 | 1 | 0 | 0 | 0 | 2 | 0 | 0/0 | 0/0 | |
| 3.U3(8).32 | 0 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| U3(8).33 | 1 | 0 | 0 | 0 | 2 | 0 | 0/0 | 0/0 | |
| U3(8):S3 | 1 | 0 | 0 | 0 | 2 | 0 | 0/0 | 0/0 | |
| 3.U3(8).S3 | 0 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| U3(8).32 | 1 | 0 | 0 | 0 | 2 | 0 | 0/0 | 0/0 | |
| U3(8).(S3 × 3) | 1 | 0 | 0 | 0 | 2 | 0 | 0/0 | 0/0 | |
| U3(9) | U3(9) | 1 | 0 | 0 | 0 | 1 | 1 | 0/0 | 0/0 |
| U3(9):2 | 0 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| U3(9):4 | 0 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| U3(11) | U3(11) | 1 | 0 | 0 | 0 | 1 | 7 | 0/0 | 0/0 |
| 3.U3(11) | 1 | 0 | 0 | 0 | 0 | 1 | 0/0 | 0/0 | |
| U3(11):2 | 1 | 0 | 0 | 0 | 1 | 2 | 0/0 | 0/0 | |
| 3.U3(11):2 | 1 | 0 | 0 | 0 | 0 | 1 | 0/0 | 0/0 | |
| U3(11):3 | 0 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| U3(11):S3 | 0 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| U3(13) | U3(13) | 1 | 0 | 0 | 0 | 1 | 0 | 0/0 | 0/0 |
| U3(13):2 | 0 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| U3(16) | U3(16) | 1 | 0 | 0 | 0 | 1 | 0 | 0/0 | 0/0 |
| U3(13):2 | 0 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| U3(13):4 | 0 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| U3(13):8 | 0 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| U4(2) | U4(2) | 1 | 1 | 1 | 0 | 5 | 33 | 20/20 | 0/0 |
| 2.U4(2) | 1 | 0 | 0 | 0 | 2 | 12 | 0/0 | 0/0 | |
| U4(2):2 | 1 | 0 | 0 | 0 | 5 | 9 | 25/25 | 0/0 | |
| 2.U4(2):2 | 1 | 0 | 0 | 0 | 1 | 1 | 0/0 | 0/0 | |
| U4(3) | U4(3) | 1 | 0 | 0 | 0 | 0 | 7 | 0/0 | 0/0 |
| 2.U4(3) | 0 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| U4(3).21 | 1 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| U4(3).4 | 1 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| U4(3).22 | 1 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| U4(3).23 | 1 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| 32.U4(3).23 | 1 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| 32.U4(3).23' | 1 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| U4(3):D8 | 1 | 0 | 0 | 0 | 11 | 0 | 0/0 | 0/0 | |
| 32.U4(3):D8 | 0 | 0 | 0 | 0 | 3 | 0 | 0/0 | 0/0 | |
| 2.U4(3).D8 | 1 | 0 | 0 | 0 | 0 | 1 | 0/0 | 0/0 | |
| U4(4) | U4(4) | 1 | 0 | 0 | 0 | 4 | 2 | 0/0 | 0/0 |
| U4(4):2 | 0 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| U4(4):4 | 0 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| U4(5) | U4(5) | 1 | 0 | 0 | 0 | 2 | 1 | 0/0 | 0/0 |
| 2.U4(5) | 1 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| U5(2) | U5(2) | 1 | 1 | 0 | 0 | 6 | 36 | 47/47 | 6/6 |
| U5(2):2 | 1 | 1 | 0 | 0 | 6 | 11 | 43/43 | 7/7 | |
| U5(3) | U5(3) | 1 | 0 | 0 | 0 | 0 | 13 | 0/0 | 4/7 |
| U5(3).2 | 0 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| U5(4) | U5(4) | 1 | 0 | 0 | 0 | 2 | 0 | 0/0 | 0/0 |
| 5.U5(4) | 1 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| U6(2) | U6(2) | 1 | 0 | 0 | 0 | 18 | 29 | 0/0 | 20/16 |
| 2.U6(2) | 1 | 0 | 0 | 0 | 8 | 12 | 0/0 | 0/0 | |
| 3.U6(2) | 1 | 0 | 0 | 0 | 6 | 20 | 0/0 | 0/0 | |
| 6.U6(2) | 1 | 0 | 0 | 0 | 4 | 4 | 0/0 | 0/0 | |
| 22.U6(2) | 1 | 0 | 0 | 0 | 1 | 0 | 0/0 | 0/0 | |
| (22 × 3).U6(2) | 1 | 0 | 0 | 0 | 2 | 1 | 0/0 | 0/0 | |
| U6(2):2 | 1 | 0 | 0 | 0 | 7 | 12 | 0/0 | 0/11 | |
| 2.U6(2).2 | 1 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| 3.U6(2):2 | 1 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| 6.U6(2).2 | 1 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| 22.U6(2):2 | 1 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| U6(2):3 | 1 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/10 | |
| 3.U6(2):3 | 1 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| 22.U6(2):3 | 1 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| U6(2):S3 | 1 | 0 | 0 | 0 | 2 | 14 | 0/0 | 0/11 | |
| 3.U6(2):S3 | 1 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| 22.U6(2):S3 | 0 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| U6(3) | U6(3) | 1 | 0 | 0 | 0 | 2 | 0 | 0/0 | 0/0 |
| U7(2) | U7(2) | 1 | 1 | 0 | 0 | 2 | 2 | 0/0 | 3/8 |
| U8(2) | U8(2) | 1 | 0 | 0 | 0 | 2 | 0 | 0/0 | 0/0 |
| U8(2):2 | 0 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| O7(3) | O7(3) | 1 | 0 | 0 | 0 | 7 | 21 | 0/0 | 0/0 |
| 2.O7(3) | 1 | 0 | 0 | 0 | 1 | 1 | 0/0 | 0/0 | |
| 3.O7(3) | 1 | 0 | 0 | 0 | 0 | 1 | 0/0 | 0/0 | |
| 6.O7(3) | 1 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| O7(3):2 | 1 | 0 | 0 | 0 | 1 | 2 | 0/0 | 0/0 | |
| 2.O7(3):2 | 1 | 0 | 0 | 0 | 0 | 1 | 0/0 | 0/0 | |
| 3O7(3):2 | 1 | 0 | 0 | 0 | 0 | 1 | 0/0 | 0/0 | |
| 6.O7(3):2 | 1 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| O8+(2) | O8+(2) | 1 | 0 | 0 | 0 | 0 | 13 | 0/0 | 0/0 |
| 2.O8+(2) | 1 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| 22.O8+(2) | 1 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| O8+(2):2 | 1 | 1 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| 2.O8+(2).2 | 1 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| O8−(2) | O8−(2) | 1 | 0 | 0 | 0 | 7 | 23 | 39/39 | 0/8 |
| O8−(2):2 | 1 | 0 | 0 | 0 | 1 | 3 | 60/60 | 0/9 | |
| O8+(3) | O8+(3) | 1 | 0 | 0 | 0 | 14 | 16 | 0/0 | 0/0 |
| 2.O8+(3) | 1 | 0 | 0 | 0 | 3 | 6 | 0/0 | 0/0 | |
| 22.O8+(3) | 1 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| O8+(3):S4 | 1 | 0 | 0 | 0 | 2 | 0 | 0/0 | 0/0 | |
| 22.O8+(3):S4 | 1 | 0 | 0 | 0 | 0 | 1 | 0/0 | 0/0 | |
| O8−(3) | O8−(3) | 1 | 0 | 0 | 0 | 1 | 2 | 0/0 | 0/0 |
| 2.O8−(3) | 1 | 0 | 0 | 0 | 0 | 3 | 0/0 | 0/0 | |
| O8−(3):21 | 1 | 0 | 0 | 0 | 1 | 1 | 0/0 | 0/0 | |
| 2.O8−(3):21 | 1 | 0 | 0 | 0 | 0 | 1 | 0/0 | 0/0 | |
| O8−(3):22 | 0 | 0 | 0 | 0 | 0 | 0 | 0/0 | 0/0 | |
| O8−(3).23 | 2 | 0 | 0 | 0 | 2 | 1 | 0/0 | 0/0 | |
| O8−(3).22 | 1 | 0 | 0 | 0 | 1 | 1 | 0/0 | 0/0 | |
| O8−(3).D8 | 0 | 0 | 0 | 0 | 0 | 1 | 0/0 | 0/0 | |
| O9(3) | O9(3) | 1 | 0 | 0 | 0 | 0 | 1 | 0/0 | 0/0 |
| 2.O9(3) | 1 | 0 | 0 | 0 | 0 | 1 | 0/0 | 0/0 | |
| O9(3):2 | 1 | 0 | 0 | 0 | 0 | 1 | 0/0 | 0/0 | |
| 2.O9(3):2 | 1 | 0 | 0 | 0 | 0 | 1 | 0/0 | 0/0 | |
| O10+(2) | O10+(2) | 1 | 0 | 0 | 0 | 7 | 17 | 0/0 | 4/9 |
| O10+(2):2 | 1 | 1 | 0 | 0 | 3 | 9 | 0/0 | 0/10 | |
| O10−(2) | O10−(2) | 1 | 0 | 0 | 0 | 2 | 9 | 0/0 | 0/10 |
| O10−(2):2 | 1 | 0 | 0 | 0 | 3 | 6 | 0/0 | 0/12 |