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Transitive Groups of degree 21

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Transitive Groups of degree 21
G Name |G| |G| fact. |Z(G)| Properties of G # fields
21T1 21 21
3 · 7
21 cyclic, semiabelian, even 86
21T2 t21n2 21
3 · 7
1 solvable, semiabelian, even 44
21T3 t21n3 42
2 · 3 · 7
3 solvable, semiabelian 170
21T4 t21n4 42
2 · 3 · 7
1 solvable, semiabelian 147
21T5 t21n5 42
2 · 3 · 7
1 solvable, semiabelian, even 54
21T6 t21n6 42
2 · 3 · 7
7 solvable, semiabelian 214
21T7 t21n7 63
32 · 7
3 solvable, semiabelian, even 142
21T8 t21n8 84
22 · 3 · 7
1 solvable, semiabelian 364
21T9 t21n9 126
2 · 32 · 7
3 solvable, semiabelian 256
21T10 t21n10 126
2 · 32 · 7
1 solvable, semiabelian, even 125
21T11 t21n11 126
2 · 32 · 7
1 solvable, semiabelian 292
21T12 t21n12 147
3 · 72
1 solvable, semiabelian, even 44
21T13 t21n13 147
3 · 72
7 solvable, semiabelian, even 68
21T14 t21n14 168
23 · 3 · 7
1 not solvable, simple, irreducible, even 253
21T15 t21n15 252
22 · 32 · 7
1 solvable, semiabelian 513
21T16 t21n16 294
2 · 3 · 72
1 solvable, semiabelian 94
21T17 t21n17 294
2 · 3 · 72
1 solvable, semiabelian, even 109
21T18 t21n18 294
2 · 3 · 72
1 solvable, semiabelian 105
21T19 t21n19 294
2 · 3 · 72
1 solvable, semiabelian 61
21T20 PGL(2, 7) 336
24 · 3 · 7
1 not solvable, primitive, irreducible 261
21T21 t21n21 441
32 · 72
1 solvable, semiabelian, even 30
21T22 t21n22 504
23 · 32 · 7
3 not solvable, even 296
21T23 t21n23 588
22 · 3 · 72
1 solvable, semiabelian 137
21T24 t21n24 882
2 · 32 · 72
1 solvable, semiabelian 65
21T25 t21n25 882
2 · 32 · 72
1 solvable, semiabelian, even 73
21T26 t21n26 882
2 · 32 · 72
1 solvable, semiabelian 66
21T27 t21n27 1008
24 · 32 · 7
1 not solvable 578
21T28 t21n28 1029
3 · 73
7 solvable, semiabelian, even 174
21T29 t21n29 1764
22 · 32 · 72
1 solvable, semiabelian 142
21T30 t21n30 2058
2 · 3 · 73
1 solvable, semiabelian, even 275
21T31 t21n31 2058
2 · 3 · 73
1 solvable, semiabelian 181
21T32 t21n32 2058
2 · 3 · 73
7 solvable, semiabelian 261
21T33 A(7) 2520
23 · 32 · 5 · 7
1 not solvable, primitive, simple, irreducible, even 368
21T34 t21n34 3087
32 · 73
1 solvable, semiabelian, even 82
21T35 t21n35 3087
32 · 73
1 solvable, semiabelian, even 173
21T36 t21n36 4116
22 · 3 · 73
1 solvable, semiabelian, even 146
21T37 t21n37 4116
22 · 3 · 73
1 solvable, semiabelian 468
21T38 S(7) 5040
24 · 32 · 5 · 7
1 not solvable, primitive, irreducible 515
21T39 t21n39 5103
36 · 7
1 solvable, semiabelian, even 127
21T40 t21n40 6174
2 · 32 · 73
1 solvable, semiabelian 261
21T41 t21n41 6174
2 · 32 · 73
1 solvable, semiabelian, even 81
21T42 t21n42 6174
2 · 32 · 73
1 solvable, semiabelian 118
21T43 t21n43 6174
2 · 32 · 73
1 solvable, semiabelian 90
21T44 t21n44 7560
23 · 33 · 5 · 7
3 not solvable, even 240
21T45 t21n45 8232
23 · 3 · 73
1 solvable, semiabelian 244
21T46 t21n46 8232
23 · 3 · 73
1 solvable, semiabelian 118
21T47 t21n47 8232
23 · 3 · 73
1 solvable, semiabelian, even 99
21T48 t21n48 9261
33 · 73
1 solvable, semiabelian, even 122
21T49 t21n49 9261
33 · 73
1 solvable, semiabelian, even 82
21T50 t21n50 10206
2 · 36 · 7
1 solvable, semiabelian 336
21T51 t21n51 10206
2 · 36 · 7
1 solvable, semiabelian, even 242
21T52 t21n52 10206
2 · 36 · 7
1 solvable, semiabelian 249
21T53 t21n53 12348
22 · 32 · 73
1 solvable, semiabelian, even 11
21T54 t21n54 12348
22 · 32 · 73
1 solvable, semiabelian, even 24
21T55 t21n55 12348
22 · 32 · 73
1 solvable, semiabelian 304
21T56 t21n56 15120
24 · 33 · 5 · 7
3 not solvable 494
21T57 t21n57 15120
24 · 33 · 5 · 7
1 not solvable 539
21T58 t21n58 15120
24 · 33 · 5 · 7
1 not solvable, even 257
21T59 t21n59 15309
37 · 7
1 solvable, semiabelian, even 104
21T60 t21n60 15309
37 · 7
1 solvable, semiabelian, even 183
21T61 t21n61 15309
37 · 7
3 solvable, semiabelian, even 89
21T62 t21n62 16464
24 · 3 · 73
1 solvable, semiabelian 266
21T63 t21n63 18522
2 · 33 · 73
1 solvable, semiabelian 76
21T64 t21n64 18522
2 · 33 · 73
1 solvable, semiabelian, even 60
21T65 t21n65 18522
2 · 33 · 73
1 solvable, semiabelian 215
21T66 t21n66 18522
2 · 33 · 73
1 solvable, semiabelian 20
21T67 PSL(3, 4)=M(21) 20160
26 · 32 · 5 · 7
1 not solvable, primitive, simple, irreducible, even 2
21T68 t21n68 20412
22 · 36 · 7
1 solvable, semiabelian 903
21T69 t21n69 24696
23 · 32 · 73
1 solvable, semiabelian 25
21T70 t21n70 24696
23 · 32 · 73
1 solvable, semiabelian 71
21T71 t21n71 24696
23 · 32 · 73
1 solvable, semiabelian 25
21T72 t21n72 24696
23 · 32 · 73
1 solvable, semiabelian, even 28
21T73 t21n73 27783
34 · 73
1 solvable, semiabelian, even 76
21T74 t21n74 30240
25 · 33 · 5 · 7
1 not solvable 986
21T75 t21n75 30618
2 · 37 · 7
1 solvable, semiabelian, even 219
21T76 t21n76 30618
2 · 37 · 7
3 solvable, semiabelian 224
21T77 t21n77 30618
2 · 37 · 7
1 solvable, semiabelian 237
21T78 t21n78 30618
2 · 37 · 7
1 solvable, semiabelian, even 140
21T79 t21n79 30618
2 · 37 · 7
1 solvable, semiabelian 236
21T80 t21n80 30618
2 · 37 · 7
1 solvable, semiabelian 300
21T81 t21n81 30618
2 · 37 · 7
1 solvable, semiabelian 140
21T82 t21n82 37044
22 · 33 · 73
1 solvable, semiabelian 133
21T83 t21n83 37044
22 · 33 · 73
1 solvable, semiabelian, even 29
21T84 t21n84 37044
22 · 33 · 73
1 solvable, semiabelian, even 27
21T85 PSigmaL(3, 4) 40320
27 · 32 · 5 · 7
1 not solvable, primitive, irreducible 4
21T86 t21n86 45927
38 · 7
3 solvable, semiabelian, even 95
21T87 t21n87 49392
24 · 32 · 73
1 solvable, semiabelian 364
21T88 t21n88 55566
2 · 34 · 73
1 solvable, semiabelian, even 16
21T89 t21n89 55566
2 · 34 · 73
1 solvable, semiabelian 49
21T90 t21n90 55566
2 · 34 · 73
1 solvable, semiabelian 171
21T91 PGL(3, 4) 60480
26 · 33 · 5 · 7
1 not solvable, primitive, irreducible, even 40
21T92 t21n92 61236
22 · 37 · 7
1 solvable, semiabelian 278
21T93 t21n93 61236
22 · 37 · 7
1 solvable, semiabelian 827
21T94 t21n94 74088
23 · 33 · 73
1 solvable, semiabelian 77
21T95 t21n95 74088
23 · 33 · 73
1 solvable, semiabelian, even 20
21T96 t21n96 74088
23 · 33 · 73
1 solvable, semiabelian 69
21T97 t21n97 74088
23 · 33 · 73
1 solvable, semiabelian 26
21T98 t21n98 91854
2 · 38 · 7
3 solvable, semiabelian 214
21T99 t21n99 91854
2 · 38 · 7
1 solvable, semiabelian, even 171
21T100 t21n100 91854
2 · 38 · 7
1 solvable, semiabelian 402
21T101 t21n101 111132
22 · 34 · 73
1 solvable, semiabelian, even 31
21T102 t21n102 111132
22 · 34 · 73
1 solvable, semiabelian 89
21T103 PGammaL(3, 4) 120960
27 · 33 · 5 · 7
1 not solvable, primitive, irreducible 139
21T104 t21n104 122472
23 · 37 · 7
1 not solvable, even 404
21T105 t21n105 122472
23 · 37 · 7
1 solvable, semiabelian, even 53
21T106 t21n106 148176
24 · 33 · 73
1 solvable, semiabelian 169
21T107 t21n107 183708
22 · 38 · 7
1 solvable, semiabelian 343
21T108 t21n108 222264
23 · 34 · 73
1 solvable, semiabelian, even 24
21T109 t21n109 222264
23 · 34 · 73
1 solvable, semiabelian 521
21T110 t21n110 222264
23 · 34 · 73
1 solvable, semiabelian 29
21T111 t21n111 244944
24 · 37 · 7
1 not solvable 288
21T112 t21n112 244944
24 · 37 · 7
1 solvable, semiabelian 208
21T113 t21n113 367416
23 · 38 · 7
1 not solvable, even 300
21T114 t21n114 367416
23 · 38 · 7
1 solvable, semiabelian, even 53
21T115 t21n115 367416
23 · 38 · 7
3 not solvable, even 192
21T116 t21n116 444528
24 · 34 · 73
1 solvable, semiabelian 703
21T117 t21n117 734832
24 · 38 · 7
1 solvable, semiabelian 212
21T118 t21n118 734832
24 · 38 · 7
1 not solvable 396
21T119 t21n119 734832
24 · 38 · 7
1 not solvable 170
21T120 t21n120 979776
26 · 37 · 7
1 solvable, semiabelian, even 281
21T121 t21n121 1837080
23 · 38 · 5 · 7
1 not solvable, even 46
21T122 t21n122 1959552
27 · 37 · 7
1 solvable, semiabelian 324
21T123 t21n123 1959552
27 · 37 · 7
1 solvable, semiabelian 583
21T124 t21n124 1959552
27 · 37 · 7
1 solvable, semiabelian, even 325
21T125 t21n125 2939328
26 · 38 · 7
1 not solvable, even 249
21T126 t21n126 2939328
26 · 38 · 7
1 not solvable, even 71
21T127 t21n127 2939328
26 · 38 · 7
1 solvable, semiabelian, even 252
21T128 t21n128 3674160
24 · 38 · 5 · 7
1 not solvable 243
21T129 t21n129 3674160
24 · 38 · 5 · 7
1 not solvable, even 196
21T130 t21n130 3674160
24 · 38 · 5 · 7
1 not solvable 290
21T131 t21n131 3919104
28 · 37 · 7
1 solvable, semiabelian 202
21T132 t21n132 5511240
23 · 39 · 5 · 7
3 not solvable, even 177
21T133 t21n133 5878656
27 · 38 · 7
1 solvable, semiabelian 310
21T134 t21n134 5878656
27 · 38 · 7
1 solvable, semiabelian, even 78
21T135 t21n135 5878656
27 · 38 · 7
1 not solvable 128
21T136 t21n136 5878656
27 · 38 · 7
1 not solvable 468
21T137 t21n137 5878656
27 · 38 · 7
1 solvable, semiabelian 120
21T138 t21n138 7348320
25 · 38 · 5 · 7
1 not solvable 457
21T139 t21n139 11022480
24 · 39 · 5 · 7
3 not solvable 398
21T140 t21n140 11022480
24 · 39 · 5 · 7
1 not solvable 379
21T141 t21n141 11022480
24 · 39 · 5 · 7
1 not solvable, even 260
21T142 t21n142 11757312
28 · 38 · 7
1 solvable, semiabelian 200
21T143 t21n143 14224896
29 · 34 · 73
1 not solvable, irreducible, even 408
21T144 t21n144 22044960
25 · 39 · 5 · 7
1 not solvable 654
21T145 t21n145 23514624
29 · 38 · 7
1 not solvable, even 442
21T146 t21n146 28449792
210 · 34 · 73
1 not solvable, irreducible 702
21T147 t21n147 47029248
210 · 38 · 7
1 not solvable 216
21T148 t21n148 352719360
29 · 39 · 5 · 7
1 not solvable, even 327
21T149 t21n149 705438720
210 · 39 · 5 · 7
1 not solvable 546
21T150 t21n150 705438720
210 · 39 · 5 · 7
1 not solvable, even 165
21T151 t21n151 705438720
210 · 39 · 5 · 7
1 not solvable 207
21T152 t21n152 1410877440
211 · 39 · 5 · 7
1 not solvable 363
21T153 t21n153 48009024000
29 · 37 · 53 · 73
1 not solvable, irreducible, even 204
21T154 t21n154 96018048000
210 · 37 · 53 · 73
1 not solvable, irreducible 15
21T155 t21n155 96018048000
210 · 37 · 53 · 73
1 not solvable, irreducible, even 6
21T156 t21n156 96018048000
210 · 37 · 53 · 73
1 not solvable, irreducible 406
21T157 t21n157 192036096000
211 · 37 · 53 · 73
1 not solvable, irreducible 19
21T158 t21n158 192036096000
211 · 37 · 53 · 73
1 not solvable, irreducible, even 7
21T159 t21n159 384072192000
212 · 37 · 53 · 73
1 not solvable, irreducible 1620
21T160 t21n160 384072192000
212 · 37 · 53 · 73
1 not solvable, irreducible 2
21T161 t21n161 384072192000
212 · 37 · 53 · 73
1 not solvable, irreducible, even 25
21T162 t21n162 768144384000
213 · 37 · 53 · 73
1 not solvable, irreducible 2138
21T163 Alt(21) 25545471085854720000
217 · 39 · 54 · 73 · 11 · 13 · 17 · 19
1 not solvable, primitive, simple, irreducible, even 10
21T164 Sym(21) 51090942171709440000
218 · 39 · 54 · 73 · 11 · 13 · 17 · 19
1 not solvable, primitive, irreducible 48

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