<< degree 16 | overview | degree 18 >>
| Transitive Groups of degree 17 | ||||||
| G | Name | |G| | |G| fact. | |Z(G)| | Properties of G | # fields |
|---|---|---|---|---|---|---|
| 17T1 | C(17)=17 | 17 |
17
|
17 | cyclic, primitive, simple, semiabelian, even | 4 |
| 17T2 | D(17)=17:2 | 34 |
2 · 17
|
1 | solvable, primitive, semiabelian, even | 80 |
| 17T3 | F68(17)=17:4 | 68 |
22 · 17
|
1 | solvable, primitive, semiabelian, even | 6 |
| 17T4 | F136(17)=17:8 | 136 |
23 · 17
|
1 | solvable, primitive, semiabelian, even | 2 |
| 17T5 | F272(17)=17:16 | 272 |
24 · 17
|
1 | solvable, primitive, semiabelian | 189 |
| 17T6 | L(17)=PSL(2,16) | 4080 |
24 · 3 · 5 · 17
|
1 | not solvable, primitive, simple, irreducible, even | 3 |
| 17T7 | L(17):2=<PZL(2,16) | 8160 |
25 · 3 · 5 · 17
|
1 | not solvable, primitive, irreducible, even | 3 |
| 17T8 | L(17):4=PYL(2,16) | 16320 |
26 · 3 · 5 · 17
|
1 | not solvable, primitive, irreducible, even | 5 |
| 17T9 | A17 | 177843714048000 |
214 · 36 · 53 · 72 · 11 · 13 · 17
|
1 | not solvable, primitive, simple, irreducible, even | 9 |
| 17T10 | S17 | 355687428096000 |
215 · 36 · 53 · 72 · 11 · 13 · 17
|
1 | not solvable, primitive, irreducible | 65 |
9 | 2,4 ms