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| Transitive Groups of degree 10 | ||||||
| G | Name | Δ |G| | |G| fact. | |Z(G)| | Properties of G | # fields |
|---|---|---|---|---|---|---|
| 10T1 | C(10)=5[x]2 | 10 |
2 · 5
|
10 | cyclic, semiabelian | 261 |
| 10T2 | D(10)=5:2 | 10 |
2 · 5
|
1 | solvable, semiabelian | 169 |
| 10T3 | D10(10)=[D(5)]2 | 20 |
22 · 5
|
2 | solvable, semiabelian | 559 |
| 10T4 | 1/2[F(5)]2 | 20 |
22 · 5
|
1 | solvable, semiabelian | 233 |
| 10T5 | F(5)[x]2 | 40 |
23 · 5
|
2 | solvable, semiabelian | 472 |
| 10T6 | [52]2 | 50 |
2 · 52
|
5 | solvable, semiabelian | 208 |
| 10T7 | A5(10) | 60 |
22 · 3 · 5
|
1 | not solvable, primitive, simple, irreducible, even | 377 |
| 10T8 | [24]5 | 80 |
24 · 5
|
1 | solvable, semiabelian, even | 510 |
| 10T9 | [1/2.D(5)2]2 | 100 |
22 · 52
|
1 | solvable, semiabelian | 293 |
| 10T10 | 1/2[D(5)2]2 | 100 |
22 · 52
|
1 | solvable, semiabelian | 217 |
| 10T11 | A(5)[x]2 | 120 |
23 · 3 · 5
|
2 | not solvable | 419 |
| 10T12 | 1/2[S(5)]2=S5(10a) | 120 |
23 · 3 · 5
|
1 | not solvable, irreducible | 598 |
| 10T13 | S5(10d) | 120 |
23 · 3 · 5
|
1 | not solvable, primitive, irreducible | 454 |
| 10T14 | [25]5 | 160 |
25 · 5
|
2 | solvable, semiabelian | 833 |
| 10T15 | [24]D(5) | 160 |
25 · 5
|
1 | solvable, semiabelian, even | 903 |
| 10T16 | 1/2[25]D(5) | 160 |
25 · 5
|
1 | solvable, semiabelian | 531 |
| 10T17 | [52:4]2 | 200 |
23 · 52
|
1 | solvable, semiabelian | 272 |
| 10T18 | [52:4]22 | 200 |
23 · 52
|
1 | solvable, semiabelian, even | 229 |
| 10T19 | [52:42]2 | 200 |
23 · 52
|
1 | solvable, semiabelian | 372 |
| 10T20 | [52:42]22 | 200 |
23 · 52
|
1 | solvable, semiabelian | 247 |
| 10T21 | [D(5)2]2 | 200 |
23 · 52
|
1 | solvable, semiabelian | 528 |
| 10T22 | S(5)[x]2 | 240 |
24 · 3 · 5
|
2 | not solvable | 721 |
| 10T23 | [25]D(5) | 320 |
26 · 5
|
2 | solvable, semiabelian | 1395 |
| 10T24 | [24]F(5) | 320 |
26 · 5
|
1 | solvable, semiabelian, even | 395 |
| 10T25 | 1/2[25]F(5) | 320 |
26 · 5
|
1 | solvable, semiabelian | 361 |
| 10T26 | L(10)=PSL(2,9) | 360 |
23 · 32 · 5
|
1 | not solvable, primitive, simple, irreducible, even | 92 |
| 10T27 | [1/2.F(5)2]2 | 400 |
24 · 52
|
1 | solvable, semiabelian | 585 |
| 10T28 | 1/2[F(5)2]2 | 400 |
24 · 52
|
1 | solvable, semiabelian, even | 324 |
| 10T29 | [25]F(5) | 640 |
27 · 5
|
2 | solvable, semiabelian | 1471 |
| 10T30 | L(10):2=PGL(2,9) | 720 |
24 · 32 · 5
|
1 | not solvable, primitive, irreducible | 94 |
| 10T31 | M(10)=L(10)'2 | 720 |
24 · 32 · 5
|
1 | not solvable, primitive, irreducible, even | 22 |
| 10T32 | S6(10)=L(10):2 | 720 |
24 · 32 · 5
|
1 | not solvable, primitive, irreducible | 264 |
| 10T33 | [F(5)2]2 | 800 |
25 · 52
|
1 | solvable, semiabelian | 470 |
| 10T34 | [24]A(5) | 960 |
26 · 3 · 5
|
1 | not solvable, even | 444 |
| 10T35 | L(10).22=P|L(2,9) | 1440 |
25 · 32 · 5
|
1 | not solvable, primitive, irreducible | 377 |
| 10T36 | [25]A(5) | 1920 |
27 · 3 · 5
|
2 | not solvable | 1380 |
| 10T37 | [24]S(5) | 1920 |
27 · 3 · 5
|
1 | not solvable, even | 793 |
| 10T38 | 1/2[25]S(5) | 1920 |
27 · 3 · 5
|
1 | not solvable | 620 |
| 10T39 | [25]S(5) | 3840 |
28 · 3 · 5
|
2 | not solvable | 1799 |
| 10T40 | [A(5)2]2 | 7200 |
25 · 32 · 52
|
1 | not solvable, irreducible | 550 |
| 10T41 | [1/2.S(5)2]2=[A(5):2]2 | 14400 |
26 · 32 · 52
|
1 | not solvable, irreducible | 643 |
| 10T42 | 1/2[S(5)2]2 | 14400 |
26 · 32 · 52
|
1 | not solvable, irreducible, even | 228 |
| 10T43 | [S(5)2]2 | 28800 |
27 · 32 · 52
|
1 | not solvable, irreducible | 1103 |
| 10T44 | A(10) | 1814400 |
27 · 34 · 52 · 7
|
1 | not solvable, primitive, simple, irreducible, even | 230 |
| 10T45 | S(10) | 3628800 |
28 · 34 · 52 · 7
|
1 | not solvable, primitive, irreducible | 643 |
9 | 3,7 ms