<< degree 5 | overview | degree 7 >>
| Transitive Groups of degree 6 | ||||||
| G | Name | |G| | |G| fact. | |Z(G)| | Properties of G | # fields |
|---|---|---|---|---|---|---|
| 6T1 | C(6) = 6 = 3[x]2 | 6 |
2 · 3
|
6 | cyclic, semiabelian | 399 |
| 6T2 | D6(6) = [3]2 | 6 |
2 · 3
|
1 | solvable, semiabelian | 221 |
| 6T3 | D(6) = S(3)[x]2 | 12 |
22 · 3
|
2 | solvable, semiabelian | 481 |
| 6T4 | A4(6) = [22]3 | 12 |
22 · 3
|
1 | solvable, semiabelian, even | 256 |
| 6T5 | F18(6) = [32]2 = 3 wr 2 | 18 |
2 · 32
|
3 | solvable, semiabelian | 257 |
| 6T6 | 2A4(6) = [23]3 = 2 wr 3 | 24 |
23 · 3
|
2 | solvable, semiabelian | 464 |
| 6T7 | S4(6d) = [22]S(3) | 24 |
23 · 3
|
1 | solvable, semiabelian, even | 335 |
| 6T8 | S4(6c) = 1/2[23]S(3) | 24 |
23 · 3
|
1 | solvable, semiabelian | 373 |
| 6T9 | F18(6):2 = [1/2.S(3)2]2 | 36 |
22 · 32
|
1 | solvable, semiabelian | 339 |
| 6T10 | F36(6) = 1/2[S(3)2]2 | 36 |
22 · 32
|
1 | solvable, semiabelian, even | 218 |
| 6T11 | 2S4(6) = [23]S(3) = 2 wr S(3) | 48 |
24 · 3
|
2 | solvable, semiabelian | 776 |
| 6T12 | L(6) = PSL(2,5) = A5(6) | 60 |
22 · 3 · 5
|
1 | not solvable, primitive, simple, irreducible, even | 353 |
| 6T13 | F36(6):2 = [S(3)2]2 = S(3) wr 2 | 72 |
23 · 32
|
1 | solvable, semiabelian | 828 |
| 6T14 | L(6):2 = PGL(2,5) = S5(6) | 120 |
23 · 3 · 5
|
1 | not solvable, primitive, irreducible | 384 |
| 6T15 | A(6) | 360 |
23 · 32 · 5
|
1 | not solvable, primitive, simple, irreducible, even | 273 |
| 6T16 | S(6) | 720 |
24 · 32 · 5
|
1 | not solvable, primitive, irreducible | 724 |
9 | 3,33 ms