List of groups of small order
| Group | Order | GAP ID (second part) | Abelian? |
|---|---|---|---|
| Trivial group | 1 | 1 | Yes |
| Cyclic group:Z2 | 2 | 1 | Yes |
| Cyclic group:Z3 | 3 | 1 | Yes |
| Cyclic group:Z4 | 4 | 1 | Yes |
| Klein four-group | 4 | 2 | Yes |
| Cyclic group:Z5 | 5 | 1 | Yes |
| Symmetric group:S3 | 6 | 2 | Yes |
| Cyclic group:Z6 | 6 | 2 | Yes |
| Cyclic group:Z7 | 7 | 1 | Yes |
| Cyclic group:Z8 | 8 | 1 | Yes |
| Direct product of Z4 and Z2 | 8 | 2 | Yes |
| Dihedral group:D8 | 8 | 3 | No |
| quaternion group | 8 | 4 | No |
| Elementary abelian group:E8 | 8 | 5 | Yes |
| Cyclic group:Z9 | 9 | 1 | Yes |
| Elementary abelian group:E9 | 9 | 2 | Yes |
| Dihedral group:D10 | 10 | 1 | No |
| Cyclic group:Z10 | 10 | 2 | Yes |
| Cyclic group:Z11 | 11 | 1 | Yes |