| T | Name(s) | |G| | Parity | |CS6(G)| | Subfields | Other Representations | Resolvents |
|---|---|---|---|---|---|---|---|
| 1 | C(6) = 6 = 3[x]2 | 6 = 2 · 3 | -1 | 6 | 2T1, 3T1 | 2: 2T1 3: 3T1 | |
| 2 | D_6(6) = [3]2 | 6 = 2 · 3 | -1 | 6 | 2T1, 3T2 | 3T2 | 2: 2T1 |
| 3 | D(6) = S(3)[x]2 | 12 = 22 · 3 | -1 | 2 | 2T1, 3T2 | 6T3, 12T3 | 2: 2T1, 2T1, 2T1 4: 4T2 6: 3T2 |
| 4 | A_4(6) = [2^2]3 | 12 = 22 · 3 | 1 | 2 | 3T1 | 4T4, 12T4 | 3: 3T1 |
| 5 | F_18(6) = [3^2]2 = 3 wr 2 | 18 = 2 · 32 | -1 | 3 | 2T1 | 9T4, 18T3 | 2: 2T1 3: 3T1 6: 3T2, 6T1 |
| 6 | 2A_4(6) = [2^3]3 = 2 wr 3 | 24 = 23 · 3 | -1 | 2 | 3T1 | 8T13, 12T6, 12T7 | 2: 2T1 3: 3T1 6: 6T1 12: 4T4 |
| 7 | S_4(6d) = [2^2]S(3) | 24 = 23 · 3 | 1 | 2 | 3T2 | 4T5, 6T8, 8T14, 12T8, 12T9 | 2: 2T1 6: 3T2 |
| 8 | S_4(6c) = 1/2[2^3]S(3) | 24 = 23 · 3 | -1 | 2 | 3T2 | 4T5, 6T7, 8T14, 12T8, 12T9 | 2: 2T1 6: 3T2 |
| 9 | F_18(6):2 = [1/2.S(3)^2]2 | 36 = 22 · 32 | -1 | 1 | 2T1 | 9T8, 12T16, 18T9, 18T11, 18T11 | 2: 2T1, 2T1, 2T1 4: 4T2 6: 3T2, 3T2 12: 6T3, 6T3 |
| 10 | F_36(6) = 1/2[S(3)^2]2 | 36 = 22 · 32 | 1 | 1 | 2T1 | 6T10, 9T9, 12T17, 12T17, 18T10 | 2: 2T1 4: 4T1 |
| 11 | 2S_4(6) = [2^3]S(3) = 2 wr S(3) | 48 = 24 · 3 | -1 | 2 | 3T2 | 6T11, 8T24, 8T24, 12T21, 12T22, 12T23, 12T23, 12T24, 12T24, 16T61 | 2: 2T1, 2T1, 2T1 4: 4T2 6: 3T2 12: 6T3 24: 4T5 |
| 12 | L(6) = PSL(2,5) = A_5(6) | 60 = 22 · 3 · 5 | 1 | 1 | 5T4, 10T7, 12T33, 15T5, 20T15 | ||
| 13 | F_36(6):2 = [S(3)^2]2 = S(3) wr 2 | 72 = 23 · 32 | -1 | 1 | 2T1 | 6T13, 9T16, 12T34, 12T34, 12T35, 12T35, 12T36, 12T36, 18T34, 18T34, 18T36 | 2: 2T1, 2T1, 2T1 4: 4T2 8: 4T3 |
| 14 | L(6):2 = PGL(2,5) = S_5(6) | 120 = 23 · 3 · 5 | -1 | 1 | 5T5, 10T12, 10T13, 12T74, 15T10, 20T30, 20T32, 20T35 | 2: 2T1 | |
| 15 | A6 | 360 = 23 · 32 · 5 | 1 | 1 | 6T15, 10T26, 15T20, 15T20, 20T89 | ||
| 16 | S6 | 720 = 24 · 32 · 5 | -1 | 1 | 6T16, 10T32, 12T183, 12T183, 15T28, 15T28, 20T145, 20T149, 20T149 | 2: 2T1 |