<< degree 8 | overview | degree 10 >>
| Transitive Groups of degree 9 | ||||||
| G | Name | Δ |G| | |G| fact. | |Z(G)| | Properties of G | # fields |
|---|---|---|---|---|---|---|
| 9T1 | C(9)=9 | 9 |
32
|
9 | cyclic, semiabelian, even | 36 |
| 9T2 | E(9)=3[x]3 | 9 |
32
|
9 | abelian, semiabelian, even | 57 |
| 9T3 | D(9)=9:2 | 18 |
2 · 32
|
1 | solvable, semiabelian, even | 86 |
| 9T4 | S(3)[x]3 | 18 |
2 · 32
|
3 | solvable, semiabelian | 414 |
| 9T5 | S(3)[1/2]S(3)=32:2 | 18 |
2 · 32
|
1 | solvable, semiabelian, even | 220 |
| 9T6 | 1/3[33]3 | 27 |
33
|
3 | nilpotent, semiabelian, even | 54 |
| 9T7 | E(9):3=[32]3 | 27 |
33
|
3 | nilpotent, semiabelian, even | 83 |
| 9T8 | S(3)[x]S(3)=E(9):D4 | 36 |
22 · 32
|
1 | solvable, semiabelian | 564 |
| 9T9 | E(9):4 | 36 |
22 · 32
|
1 | solvable, primitive, semiabelian, even | 113 |
| 9T10 | [32]S(3)6 | 54 |
2 · 33
|
1 | solvable, semiabelian, even | 140 |
| 9T11 | E(9):6=1/2[32:2]S(3) | 54 |
2 · 33
|
1 | solvable, semiabelian, even | 144 |
| 9T12 | [32]S(3) | 54 |
2 · 33
|
3 | solvable, semiabelian | 180 |
| 9T13 | E(9):D6=[32:2]3=[1/2.S(3)2]3 | 54 |
2 · 33
|
1 | solvable, semiabelian | 156 |
| 9T14 | M(9)=E(9):Q8 | 72 |
23 · 32
|
1 | solvable, primitive, semiabelian, even | 103 |
| 9T15 | E(9):8 | 72 |
23 · 32
|
1 | solvable, primitive, semiabelian | 81 |
| 9T16 | E(9):D8 | 72 |
23 · 32
|
1 | solvable, primitive, semiabelian | 222 |
| 9T17 | [33]3=3wr3 | 81 |
34
|
3 | nilpotent, semiabelian, even | 58 |
| 9T18 | E(9):D12=[32:2]S(3)=[1/2.S(3)2]S(3) | 108 |
22 · 33
|
1 | solvable, semiabelian | 431 |
| 9T19 | E(9):2D8 | 144 |
24 · 32
|
1 | solvable, primitive, semiabelian | 179 |
| 9T20 | [33]S(3)=3wrS(3) | 162 |
2 · 34
|
3 | solvable, semiabelian | 195 |
| 9T21 | 1/2.[33:2]S(3) | 162 |
2 · 34
|
1 | solvable, semiabelian, even | 262 |
| 9T22 | [33:2]3 | 162 |
2 · 34
|
1 | solvable, semiabelian | 180 |
| 9T23 | E(9):2A4 | 216 |
23 · 33
|
1 | solvable, primitive, even | 87 |
| 9T24 | [33:2]S(3) | 324 |
22 · 34
|
1 | solvable, semiabelian | 502 |
| 9T25 | [1/2.S(3)3]3 | 324 |
22 · 34
|
1 | solvable, semiabelian, even | 218 |
| 9T26 | E(9):2S4 | 432 |
24 · 33
|
1 | solvable, primitive | 169 |
| 9T27 | L(9)=PSL(2,8) | 504 |
23 · 32 · 7
|
1 | not solvable, primitive, simple, irreducible, even | 94 |
| 9T28 | [S(3)3]3=S(3)wr3 | 648 |
23 · 34
|
1 | solvable, semiabelian | 725 |
| 9T29 | [1/2.S(3)3]S(3) | 648 |
23 · 34
|
1 | solvable, semiabelian | 306 |
| 9T30 | 1/2[S(3)3]S(3) | 648 |
23 · 34
|
1 | solvable, semiabelian, even | 401 |
| 9T31 | [S(3)3]S(3)=S(3)wrS(3) | 1296 |
24 · 34
|
1 | solvable, semiabelian | 896 |
| 9T32 | L(9):3=P|L(2,8) | 1512 |
23 · 33 · 7
|
1 | not solvable, primitive, irreducible, even | 296 |
| 9T33 | A(9) | 181440 |
26 · 34 · 5 · 7
|
1 | not solvable, primitive, simple, irreducible, even | 222 |
| 9T34 | S(9) | 362880 |
27 · 34 · 5 · 7
|
1 | not solvable, primitive, irreducible | 1000 |
9 | 2,8 ms