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Transitive Groups of degree 15

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Transitive Groups of degree 15
G Δ Name |G| |G| fact. |Z(G)| Properties of G # fields
15T65 1/2[1/2.F(5)3]S(3) 12000
25 · 3 · 53
1 solvable, semiabelian 279
15T35 1/2[34:2]D(5) 810
2 · 34 · 5
1 solvable, semiabelian 236
15T42 1/2[34:2]F(5) 1620
22 · 34 · 5
1 solvable, semiabelian, even 210
15T62 1/2[34:2]S(5) 9720
23 · 35 · 5
1 not solvable, even 375
15T45 1/2[35:2]D(5) 2430
2 · 35 · 5
1 solvable, semiabelian 168
15T54 1/2[35:2]F(5) 4860
22 · 35 · 5
1 solvable, semiabelian, even 85
15T77 1/2[35:2]S(5) 29160
23 · 36 · 5
1 not solvable, even 320
15T17 1/2[52:4]S(3) 300
22 · 3 · 52
1 solvable, semiabelian, even 110
15T31 1/2[53:2]S(3) 750
2 · 3 · 53
1 solvable, semiabelian 109
15T37 1/2[53:4]S(3) 1500
22 · 3 · 53
1 solvable, semiabelian, even 202
15T94 1/2[A(5)3:2]S(3) 1296000
27 · 34 · 53
1 not solvable, irreducible, even 53
15T58 1/2[D(5)3:2]S(3) 6000
24 · 3 · 53
1 solvable, semiabelian, even 252
15T39 [1/2.D(5)3]3 1500
22 · 3 · 53
1 solvable, semiabelian, even 111
15T51 [1/2.D(5)3]S(3) 3000
23 · 3 · 53
1 solvable, semiabelian 265
15T48 1/2[D(5)3]S(3) 3000
23 · 3 · 53
1 solvable, semiabelian 193
15T67 [1/2.F(5)3]3 12000
25 · 3 · 53
1 solvable, semiabelian, even 352
15T74 [1/2.F(5)3]S(3) 24000
26 · 3 · 53
1 solvable, semiabelian 366
15T73 1/2[F(5)3]S(3) 24000
26 · 3 · 53
1 solvable, semiabelian, even 336
15T71 [1/2.S(3)5]5 19440
24 · 35 · 5
1 solvable, semiabelian, even 104
15T88 [1/2.S(3)5]A(5) 233280
26 · 36 · 5
1 not solvable, even 159
15T80 [1/2.S(3)5]D(5) 38880
25 · 35 · 5
1 solvable, semiabelian, even 109
15T79 1/2[S(3)5]D(5) 38880
25 · 35 · 5
1 solvable, semiabelian 208
15T85 [1/2.S(3)5]F(5) 77760
26 · 35 · 5
1 solvable, semiabelian 138
15T84 1/2[S(3)5]F(5) 77760
26 · 35 · 5
1 solvable, semiabelian, even 152
15T91 [1/2.S(3)5]S(5) 466560
27 · 36 · 5
1 not solvable 185
15T89 1/2[S(3)5]S(5) 466560
27 · 36 · 5
1 not solvable, even 244
15T98 [1/2.S(5)3]3 2592000
28 · 34 · 53
1 not solvable, irreducible, even 80
15T100 [1/2.S(5)3]S(3) 5184000
29 · 34 · 53
1 not solvable, irreducible 211
15T99 1/2[S(5)3]S(3) 5184000
29 · 34 · 53
1 not solvable, irreducible, even 94
15T57 [1/4.F(5)3]3 6000
24 · 3 · 53
1 solvable, semiabelian, even 167
15T66 [1/4.F(5)3]S(3) 12000
25 · 3 · 53
1 solvable, semiabelian 266
15T33 [34:2]5 810
2 · 34 · 5
1 solvable, semiabelian 121
15T61 [34:2]A(5) 9720
23 · 35 · 5
1 not solvable 236
15T43 [34:2]D(5) 1620
22 · 34 · 5
1 solvable, semiabelian 432
15T52 [34:2]F(5) 3240
23 · 34 · 5
1 solvable, semiabelian 297
15T70 [34:2]S(5) 19440
24 · 35 · 5
1 not solvable 335
15T26 [34]5 405
34 · 5
1 solvable, semiabelian, even 78
15T53 [34]A(5) 4860
22 · 35 · 5
1 not solvable, even 265
15T34 [34]D(5) 810
2 · 34 · 5
1 solvable, semiabelian, even 214
15T41 [34]F(5) 1620
22 · 34 · 5
1 solvable, semiabelian 181
15T63 [34]S(5) 9720
23 · 35 · 5
1 not solvable 339
15T44 [35:2]5 2430
2 · 35 · 5
1 solvable, semiabelian 144
15T76 [35:2]A(5) 29160
23 · 36 · 5
1 not solvable 307
15T55 [35:2]D(5) 4860
22 · 35 · 5
1 solvable, semiabelian 370
15T64 [35:2]F(5) 9720
23 · 35 · 5
1 solvable, semiabelian 271
15T83 [35:2]S(5) 58320
24 · 36 · 5
1 not solvable 410
15T36 [35]5=3wr5 1215
35 · 5
3 solvable, semiabelian, even 96
15T69 [35]A(5)=3wrA(5) 14580
22 · 36 · 5
3 not solvable, even 211
15T46 [35]D(5)=3wrD(5) 2430
2 · 35 · 5
3 solvable, semiabelian, even 165
15T56 [35]F(5)=3wrF(5) 4860
22 · 35 · 5
3 solvable, semiabelian 198
15T78 [35]S(5)=3wrS(5) 29160
23 · 36 · 5
3 not solvable 305
15T15 3A5(15)=[3]A(5)=GL(2,4) 180
22 · 32 · 5
3 not solvable, even 238
15T21 3S5(15) 360
23 · 32 · 5
1 not solvable, even 251
15T14 52:2[1/2]S(3) 150
2 · 3 · 52
1 solvable, semiabelian 176
15T12 [52:2]3 150
2 · 3 · 52
1 solvable, semiabelian, even 89
15T18 [52:2]S(3) 300
22 · 3 · 52
1 solvable, semiabelian 235
15T9 [52]3 75
3 · 52
1 solvable, semiabelian, even 97
15T19 [52:4]3 300
22 · 3 · 52
1 solvable, semiabelian 113
15T27 [52:4]S(3) 600
23 · 3 · 52
1 solvable, semiabelian 221
15T13 [52]S(3) 150
2 · 3 · 52
1 solvable, semiabelian 173
15T30 [53:2]3 750
2 · 3 · 53
1 solvable, semiabelian, even 146
15T40 [53:2]S(3) 1500
22 · 3 · 53
1 solvable, semiabelian 274
15T25 [53]3=5wr3 375
3 · 53
5 solvable, semiabelian, even 85
15T38 [53:4]3 1500
22 · 3 · 53
1 solvable, semiabelian 130
15T49 [53:4]S(3) 3000
23 · 3 · 53
1 solvable, semiabelian 170
15T32 [53]S(3) 750
2 · 3 · 53
5 solvable, semiabelian 200
15T4 5[x]S(3) 30
2 · 3 · 5
5 solvable, semiabelian 186
15T103 A(15) 653837184000
210 · 36 · 53 · 72 · 11 · 13
1 not solvable, primitive, simple, irreducible, even 11
15T5 A5(15) 60
22 · 3 · 5
1 not solvable, simple, irreducible, even 104
15T95 [A(5)3:2]3 1296000
27 · 34 · 53
1 not solvable, irreducible 98
15T97 [A(5)3:2]S(3) 2592000
28 · 34 · 53
1 not solvable, irreducible 209
15T92 [A(5)3]3=A(5)wr3 648000
26 · 34 · 53
1 not solvable, irreducible, even 26
15T96 [A(5)3]S(3)=A(5)wrS(3) 1296000
27 · 34 · 53
1 not solvable, irreducible 76
15T16 A(5)[x]3 180
22 · 32 · 5
3 not solvable, even 204
15T23 A(5)[x]S(3) 360
23 · 32 · 5
1 not solvable 206
15T20 A6(15) 360
23 · 32 · 5
1 not solvable, primitive, simple, irreducible, even 100
15T47 A7(15) 2520
23 · 32 · 5 · 7
1 not solvable, primitive, simple, irreducible, even 80
15T1 C(15)=5[x]3 15
3 · 5
15 cyclic, semiabelian, even 61
15T2 D(15) 30
2 · 3 · 5
1 solvable, semiabelian 157
15T59 [D(5)3:2]3 6000
24 · 3 · 53
1 solvable, semiabelian 149
15T68 [D(5)3:2]S(3) 12000
25 · 3 · 53
1 solvable, semiabelian 246
15T50 [D(5)3]3=D(5)wr3 3000
23 · 3 · 53
1 solvable, semiabelian, even 205
15T60 [D(5)3]S(3)=D(5)wrS(3) 6000
24 · 3 · 53
1 solvable, semiabelian 434
15T3 D(5)[x]3 30
2 · 3 · 5
3 solvable, semiabelian, even 150
15T7 D(5)[x]S(3) 60
22 · 3 · 5
1 solvable, semiabelian 290
15T6 F(5)[1/2]S(3) 60
22 · 3 · 5
1 solvable, semiabelian, even 157
15T75 [F(5)3]3=F(5)wr3 24000
26 · 3 · 53
1 solvable, semiabelian 244
15T82 [F(5)3]S(3)=F(5)wrS(3) 48000
27 · 3 · 53
1 solvable, semiabelian 419
15T8 F(5)[x]3 60
22 · 3 · 5
3 solvable, semiabelian 227
15T11 F(5)[x]S(3) 120
23 · 3 · 5
1 solvable, semiabelian 249
15T72 L(15)=A8(15)=PSL(4,2) 20160
26 · 32 · 5 · 7
1 not solvable, primitive, simple, irreducible, even 115
15T104 S(15) 1307674368000
211 · 36 · 53 · 72 · 11 · 13
1 not solvable, primitive, irreducible 109
15T81 [S(3)5]5=S(3)wr5 38880
25 · 35 · 5
1 solvable, semiabelian 297
15T90 [S(3)5]A(5)=S(3)wrA(5) 466560
27 · 36 · 5
1 not solvable 500
15T86 [S(3)5]D(5)=S(3)wrD(5) 77760
26 · 35 · 5
1 solvable, semiabelian 413
15T87 [S(3)5]F(5)=S(3)wrF(5) 155520
27 · 35 · 5
1 solvable, semiabelian 381
15T93 [S(3)5]S(5)=S(3)wrS(5) 933120
28 · 36 · 5
1 not solvable 490
15T22 S(5)[1/2]S(3) 360
23 · 32 · 5
1 not solvable, even 171
15T10 S5(15) 120
23 · 3 · 5
1 not solvable, irreducible, even 219
15T101 [S(5)3]3=S(5)wr3 5184000
29 · 34 · 53
1 not solvable, irreducible 497
15T102 [S(5)3]S(3)=S(5)wrS(3) 10368000
210 · 34 · 53
1 not solvable, irreducible 739
15T24 S(5)[x]3 360
23 · 32 · 5
3 not solvable 331
15T29 S(5)[x]S(3) 720
24 · 32 · 5
1 not solvable 390
15T28 S6(15) 720
24 · 32 · 5
1 not solvable, primitive, irreducible, even 308

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