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| Transitive Groups of degree 15 | ||||||
| Δ G | Name | |G| | |G| fact. | |Z(G)| | Properties of G | # fields |
|---|---|---|---|---|---|---|
| 15T1 | C(15)=5[x]3 | 15 |
3 · 5
|
15 | cyclic, semiabelian, even | 70 |
| 15T2 | D(15) | 30 |
2 · 3 · 5
|
1 | solvable, semiabelian | 186 |
| 15T3 | D(5)[x]3 | 30 |
2 · 3 · 5
|
3 | solvable, semiabelian, even | 152 |
| 15T4 | 5[x]S(3) | 30 |
2 · 3 · 5
|
5 | solvable, semiabelian | 198 |
| 15T5 | A5(15) | 60 |
22 · 3 · 5
|
1 | not solvable, simple, irreducible, even | 108 |
| 15T6 | F(5)[1/2]S(3) | 60 |
22 · 3 · 5
|
1 | solvable, semiabelian, even | 211 |
| 15T7 | D(5)[x]S(3) | 60 |
22 · 3 · 5
|
1 | solvable, semiabelian | 297 |
| 15T8 | F(5)[x]3 | 60 |
22 · 3 · 5
|
3 | solvable, semiabelian | 227 |
| 15T9 | [52]3 | 75 |
3 · 52
|
1 | solvable, semiabelian, even | 123 |
| 15T10 | S5(15) | 120 |
23 · 3 · 5
|
1 | not solvable, irreducible, even | 230 |
| 15T11 | F(5)[x]S(3) | 120 |
23 · 3 · 5
|
1 | solvable, semiabelian | 324 |
| 15T12 | [52:2]3 | 150 |
2 · 3 · 52
|
1 | solvable, semiabelian, even | 101 |
| 15T13 | [52]S(3) | 150 |
2 · 3 · 52
|
1 | solvable, semiabelian | 207 |
| 15T14 | 52:2[1/2]S(3) | 150 |
2 · 3 · 52
|
1 | solvable, semiabelian | 209 |
| 15T15 | 3A5(15)=[3]A(5)=GL(2,4) | 180 |
22 · 32 · 5
|
3 | not solvable, even | 238 |
| 15T16 | A(5)[x]3 | 180 |
22 · 32 · 5
|
3 | not solvable, even | 204 |
| 15T17 | 1/2[52:4]S(3) | 300 |
22 · 3 · 52
|
1 | solvable, semiabelian, even | 177 |
| 15T18 | [52:2]S(3) | 300 |
22 · 3 · 52
|
1 | solvable, semiabelian | 238 |
| 15T19 | [52:4]3 | 300 |
22 · 3 · 52
|
1 | solvable, semiabelian | 136 |
| 15T20 | A6(15) | 360 |
23 · 32 · 5
|
1 | not solvable, primitive, simple, irreducible, even | 113 |
| 15T21 | 3S5(15) | 360 |
23 · 32 · 5
|
1 | not solvable, even | 255 |
| 15T22 | S(5)[1/2]S(3) | 360 |
23 · 32 · 5
|
1 | not solvable, even | 196 |
| 15T23 | A(5)[x]S(3) | 360 |
23 · 32 · 5
|
1 | not solvable | 207 |
| 15T24 | S(5)[x]3 | 360 |
23 · 32 · 5
|
3 | not solvable | 416 |
| 15T25 | [53]3=5wr3 | 375 |
3 · 53
|
5 | solvable, semiabelian, even | 127 |
| 15T26 | [34]5 | 405 |
34 · 5
|
1 | solvable, semiabelian, even | 100 |
| 15T27 | [52:4]S(3) | 600 |
23 · 3 · 52
|
1 | solvable, semiabelian | 285 |
| 15T28 | S6(15) | 720 |
24 · 32 · 5
|
1 | not solvable, primitive, irreducible, even | 319 |
| 15T29 | S(5)[x]S(3) | 720 |
24 · 32 · 5
|
1 | not solvable | 426 |
| 15T30 | [53:2]3 | 750 |
2 · 3 · 53
|
1 | solvable, semiabelian, even | 175 |
| 15T31 | 1/2[53:2]S(3) | 750 |
2 · 3 · 53
|
1 | solvable, semiabelian | 109 |
| 15T32 | [53]S(3) | 750 |
2 · 3 · 53
|
5 | solvable, semiabelian | 232 |
| 15T33 | [34:2]5 | 810 |
2 · 34 · 5
|
1 | solvable, semiabelian | 154 |
| 15T34 | [34]D(5) | 810 |
2 · 34 · 5
|
1 | solvable, semiabelian, even | 214 |
| 15T35 | 1/2[34:2]D(5) | 810 |
2 · 34 · 5
|
1 | solvable, semiabelian | 240 |
| 15T36 | [35]5=3wr5 | 1215 |
35 · 5
|
3 | solvable, semiabelian, even | 126 |
| 15T37 | 1/2[53:4]S(3) | 1500 |
22 · 3 · 53
|
1 | solvable, semiabelian, even | 322 |
| 15T38 | [53:4]3 | 1500 |
22 · 3 · 53
|
1 | solvable, semiabelian | 169 |
| 15T39 | [1/2.D(5)3]3 | 1500 |
22 · 3 · 53
|
1 | solvable, semiabelian, even | 112 |
| 15T40 | [53:2]S(3) | 1500 |
22 · 3 · 53
|
1 | solvable, semiabelian | 282 |
| 15T41 | [34]F(5) | 1620 |
22 · 34 · 5
|
1 | solvable, semiabelian | 181 |
| 15T42 | 1/2[34:2]F(5) | 1620 |
22 · 34 · 5
|
1 | solvable, semiabelian, even | 210 |
| 15T43 | [34:2]D(5) | 1620 |
22 · 34 · 5
|
1 | solvable, semiabelian | 432 |
| 15T44 | [35:2]5 | 2430 |
2 · 35 · 5
|
1 | solvable, semiabelian | 147 |
| 15T45 | 1/2[35:2]D(5) | 2430 |
2 · 35 · 5
|
1 | solvable, semiabelian | 174 |
| 15T46 | [35]D(5)=3wrD(5) | 2430 |
2 · 35 · 5
|
3 | solvable, semiabelian, even | 184 |
| 15T47 | A7(15) | 2520 |
23 · 32 · 5 · 7
|
1 | not solvable, primitive, simple, irreducible, even | 80 |
| 15T48 | 1/2[D(5)3]S(3) | 3000 |
23 · 3 · 53
|
1 | solvable, semiabelian | 197 |
| 15T49 | [53:4]S(3) | 3000 |
23 · 3 · 53
|
1 | solvable, semiabelian | 292 |
| 15T50 | [D(5)3]3=D(5)wr3 | 3000 |
23 · 3 · 53
|
1 | solvable, semiabelian, even | 585 |
| 15T51 | [1/2.D(5)3]S(3) | 3000 |
23 · 3 · 53
|
1 | solvable, semiabelian | 270 |
| 15T52 | [34:2]F(5) | 3240 |
23 · 34 · 5
|
1 | solvable, semiabelian | 323 |
| 15T53 | [34]A(5) | 4860 |
22 · 35 · 5
|
1 | not solvable, even | 265 |
| 15T54 | 1/2[35:2]F(5) | 4860 |
22 · 35 · 5
|
1 | solvable, semiabelian, even | 163 |
| 15T55 | [35:2]D(5) | 4860 |
22 · 35 · 5
|
1 | solvable, semiabelian | 382 |
| 15T56 | [35]F(5)=3wrF(5) | 4860 |
22 · 35 · 5
|
3 | solvable, semiabelian | 209 |
| 15T57 | [1/4.F(5)3]3 | 6000 |
24 · 3 · 53
|
1 | solvable, semiabelian, even | 261 |
| 15T58 | 1/2[D(5)3:2]S(3) | 6000 |
24 · 3 · 53
|
1 | solvable, semiabelian, even | 303 |
| 15T59 | [D(5)3:2]3 | 6000 |
24 · 3 · 53
|
1 | solvable, semiabelian | 250 |
| 15T60 | [D(5)3]S(3)=D(5)wrS(3) | 6000 |
24 · 3 · 53
|
1 | solvable, semiabelian | 1064 |
| 15T61 | [34:2]A(5) | 9720 |
23 · 35 · 5
|
1 | not solvable | 264 |
| 15T62 | 1/2[34:2]S(5) | 9720 |
23 · 35 · 5
|
1 | not solvable, even | 375 |
| 15T63 | [34]S(5) | 9720 |
23 · 35 · 5
|
1 | not solvable | 340 |
| 15T64 | [35:2]F(5) | 9720 |
23 · 35 · 5
|
1 | solvable, semiabelian | 309 |
| 15T65 | 1/2[1/2.F(5)3]S(3) | 12000 |
25 · 3 · 53
|
1 | solvable, semiabelian | 411 |
| 15T66 | [1/4.F(5)3]S(3) | 12000 |
25 · 3 · 53
|
1 | solvable, semiabelian | 325 |
| 15T67 | [1/2.F(5)3]3 | 12000 |
25 · 3 · 53
|
1 | solvable, semiabelian, even | 531 |
| 15T68 | [D(5)3:2]S(3) | 12000 |
25 · 3 · 53
|
1 | solvable, semiabelian | 385 |
| 15T69 | [35]A(5)=3wrA(5) | 14580 |
22 · 36 · 5
|
3 | not solvable, even | 220 |
| 15T70 | [34:2]S(5) | 19440 |
24 · 35 · 5
|
1 | not solvable | 391 |
| 15T71 | [1/2.S(3)5]5 | 19440 |
24 · 35 · 5
|
1 | solvable, semiabelian, even | 179 |
| 15T72 | L(15)=A8(15)=PSL(4,2) | 20160 |
26 · 32 · 5 · 7
|
1 | not solvable, primitive, simple, irreducible, even | 115 |
| 15T73 | 1/2[F(5)3]S(3) | 24000 |
26 · 3 · 53
|
1 | solvable, semiabelian, even | 494 |
| 15T74 | [1/2.F(5)3]S(3) | 24000 |
26 · 3 · 53
|
1 | solvable, semiabelian | 602 |
| 15T75 | [F(5)3]3=F(5)wr3 | 24000 |
26 · 3 · 53
|
1 | solvable, semiabelian | 354 |
| 15T76 | [35:2]A(5) | 29160 |
23 · 36 · 5
|
1 | not solvable | 338 |
| 15T77 | 1/2[35:2]S(5) | 29160 |
23 · 36 · 5
|
1 | not solvable, even | 336 |
| 15T78 | [35]S(5)=3wrS(5) | 29160 |
23 · 36 · 5
|
3 | not solvable | 307 |
| 15T79 | 1/2[S(3)5]D(5) | 38880 |
25 · 35 · 5
|
1 | solvable, semiabelian | 275 |
| 15T80 | [1/2.S(3)5]D(5) | 38880 |
25 · 35 · 5
|
1 | solvable, semiabelian, even | 216 |
| 15T81 | [S(3)5]5=S(3)wr5 | 38880 |
25 · 35 · 5
|
1 | solvable, semiabelian | 373 |
| 15T82 | [F(5)3]S(3)=F(5)wrS(3) | 48000 |
27 · 3 · 53
|
1 | solvable, semiabelian | 466 |
| 15T83 | [35:2]S(5) | 58320 |
24 · 36 · 5
|
1 | not solvable | 454 |
| 15T84 | 1/2[S(3)5]F(5) | 77760 |
26 · 35 · 5
|
1 | solvable, semiabelian, even | 224 |
| 15T85 | [1/2.S(3)5]F(5) | 77760 |
26 · 35 · 5
|
1 | solvable, semiabelian | 199 |
| 15T86 | [S(3)5]D(5)=S(3)wrD(5) | 77760 |
26 · 35 · 5
|
1 | solvable, semiabelian | 513 |
| 15T87 | [S(3)5]F(5)=S(3)wrF(5) | 155520 |
27 · 35 · 5
|
1 | solvable, semiabelian | 510 |
| 15T88 | [1/2.S(3)5]A(5) | 233280 |
26 · 36 · 5
|
1 | not solvable, even | 227 |
| 15T89 | 1/2[S(3)5]S(5) | 466560 |
27 · 36 · 5
|
1 | not solvable, even | 356 |
| 15T90 | [S(3)5]A(5)=S(3)wrA(5) | 466560 |
27 · 36 · 5
|
1 | not solvable | 536 |
| 15T91 | [1/2.S(3)5]S(5) | 466560 |
27 · 36 · 5
|
1 | not solvable | 367 |
| 15T92 | [A(5)3]3=A(5)wr3 | 648000 |
26 · 34 · 53
|
1 | not solvable, irreducible, even | 185 |
| 15T93 | [S(3)5]S(5)=S(3)wrS(5) | 933120 |
28 · 36 · 5
|
1 | not solvable | 573 |
| 15T94 | 1/2[A(5)3:2]S(3) | 1296000 |
27 · 34 · 53
|
1 | not solvable, irreducible, even | 372 |
| 15T95 | [A(5)3:2]3 | 1296000 |
27 · 34 · 53
|
1 | not solvable, irreducible | 360 |
| 15T96 | [A(5)3]S(3)=A(5)wrS(3) | 1296000 |
27 · 34 · 53
|
1 | not solvable, irreducible | 291 |
| 15T97 | [A(5)3:2]S(3) | 2592000 |
28 · 34 · 53
|
1 | not solvable, irreducible | 383 |
| 15T98 | [1/2.S(5)3]3 | 2592000 |
28 · 34 · 53
|
1 | not solvable, irreducible, even | 312 |
| 15T99 | 1/2[S(5)3]S(3) | 5184000 |
29 · 34 · 53
|
1 | not solvable, irreducible, even | 244 |
| 15T100 | [1/2.S(5)3]S(3) | 5184000 |
29 · 34 · 53
|
1 | not solvable, irreducible | 530 |
| 15T101 | [S(5)3]3=S(5)wr3 | 5184000 |
29 · 34 · 53
|
1 | not solvable, irreducible | 1236 |
| 15T102 | [S(5)3]S(3)=S(5)wrS(3) | 10368000 |
210 · 34 · 53
|
1 | not solvable, irreducible | 2086 |
| 15T103 | A(15) | 653837184000 |
210 · 36 · 53 · 72 · 11 · 13
|
1 | not solvable, primitive, simple, irreducible, even | 11 |
| 15T104 | S(15) | 1307674368000 |
211 · 36 · 53 · 72 · 11 · 13
|
1 | not solvable, primitive, irreducible | 113 |
9 | 2,67 ms