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| Transitive Groups of degree 5 | ||||||
| G | Name | |G| | |G| fact. | |Z(G)| | Properties of G | # fields |
|---|---|---|---|---|---|---|
| 5T1 | C(5) = 5 | 5 |
5
|
5 | cyclic, primitive, simple, semiabelian, even | 159 |
| 5T2 | D(5) = 5:2 | 10 |
2 · 5
|
1 | solvable, primitive, semiabelian, even | 362 |
| 5T3 | F(5) = 5:4 | 20 |
22 · 5
|
1 | solvable, primitive, semiabelian | 282 |
| 5T4 | A(5) | 60 |
22 · 3 · 5
|
1 | not solvable, primitive, simple, irreducible, even | 376 |
| 5T5 | S(5) | 120 |
23 · 3 · 5
|
1 | not solvable, primitive, irreducible | 591 |
9 | 1,75 ms