| T | Name(s) | |G| | Parity | |CS7(G)| | Other Representations | Resolvents |
|---|---|---|---|---|---|---|
| 1 | C(7) = 7 | 7 | 1 | 7 | ||
| 2 | D(7) = 7:2 | 14 = 2 · 7 | -1 | 1 | 14T2 | 2: 2T1 |
| 3 | F_21(7) = 7:3 | 21 = 3 · 7 | 1 | 1 | 21T2 | 3: 3T1 |
| 4 | F_42(7) = 7:6 | 42 = 2 · 3 · 7 | -1 | 1 | 14T4, 21T4 | 2: 2T1 3: 3T1 6: 6T1 |
| 5 | L(7) = L(3,2) | 168 = 23 · 3 · 7 | 1 | 1 | 7T5, 8T37, 14T10, 14T10, 21T14 | |
| 6 | A7 | 2520 = 23 · 32 · 5 · 7 | 1 | 1 | 15T47, 15T47, 21T33 | |
| 7 | S7 | 5040 = 24 · 32 · 5 · 7 | -1 | 1 | 14T46, 21T38 | 2: 2T1 |