<< degree 6 | overview | degree 8 >>
| Transitive Groups of degree 7 | ||||||
| G | Name | |G| | |G| fact. | |Z(G)| | Properties of G | # fields |
|---|---|---|---|---|---|---|
| 7T1 | C(7) = 7 | 7 |
7
|
7 | cyclic, primitive, simple, semiabelian, even | 94 |
| 7T2 | D(7) = 7:2 | 14 |
2 · 7
|
1 | solvable, primitive, semiabelian | 66 |
| 7T3 | F21(7) = 7:3 | 21 |
3 · 7
|
1 | solvable, primitive, semiabelian, even | 75 |
| 7T4 | F42(7) = 7:6 | 42 |
2 · 3 · 7
|
1 | solvable, primitive, semiabelian | 196 |
| 7T5 | L(7) = L(3,2) | 168 |
23 · 3 · 7
|
1 | not solvable, primitive, simple, irreducible, even | 375 |
| 7T6 | A(7) | 2520 |
23 · 32 · 5 · 7
|
1 | not solvable, primitive, simple, irreducible, even | 383 |
| 7T7 | S(7) | 5040 |
24 · 32 · 5 · 7
|
1 | not solvable, primitive, irreducible | 504 |
9 | 2,15 ms