| Transitive Groups of degree 23 | ||||||
| G | Name | ∇ |G| | |G| fact. | |Z(G)| | Properties of G | # fields |
|---|---|---|---|---|---|---|
| 23T7 | S(23) | 25852016738884976640000 |
219 · 39 · 54 · 73 · 112 · 13 · 17 · 19 · 23
|
1 | not solvable, primitive, irreducible | 79 |
| 23T6 | A(23) | 12926008369442488320000 |
218 · 39 · 54 · 73 · 112 · 13 · 17 · 19 · 23
|
1 | not solvable, primitive, simple, irreducible, even | 11 |
| 23T5 | M(23) | 10200960 |
27 · 32 · 5 · 7 · 11 · 23
|
1 | not solvable, primitive, simple, irreducible, even | 0 |
| 23T4 | AGL(1,23) | 506 |
2 · 11 · 23
|
1 | solvable, primitive, semiabelian | 199 |
| 23T3 | F(23)=23:11 | 253 |
11 · 23
|
1 | solvable, primitive, semiabelian, even | 99 |
| 23T2 | D(23)=23:2 | 46 |
2 · 23
|
1 | solvable, primitive, semiabelian | 10 |
| 23T1 | C(23) | 23 |
23
|
23 | cyclic, primitive, simple, semiabelian, even | 41 |
8 | 3,44 ms