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Transitive Groups of degree 12

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Transitive Groups of degree 12
Δ G Name |G| |G| fact. |Z(G)| Properties of G # fields
12T1 C(4)[x]C(3) 12
22 · 3
12 cyclic, semiabelian 194
12T2 E(4)[x]C(3)=6x2 12
22 · 3
12 abelian, semiabelian, even 226
12T3 D6(6)[x]2=1/2[3:2]E(4) 12
22 · 3
2 solvable, semiabelian, even 623
12T4 A4(12) 12
22 · 3
1 solvable, semiabelian, even 209
12T5 1/2[3:2]4 12
22 · 3
2 solvable, semiabelian 196
12T6 A4(12)x2 24
23 · 3
2 solvable, semiabelian, even 513
12T7 A4(6)[x]2=[1/8.26]3 24
23 · 3
2 solvable, semiabelian, even 466
12T8 S4(12d) 24
23 · 3
1 solvable, semiabelian 529
12T9 1/2[1/8.26]S(3)=S4(12e) 24
23 · 3
1 solvable, semiabelian, even 507
12T10 S(3)[x]E(4) 24
23 · 3
4 solvable, semiabelian, even 793
12T11 S(3)[x]C(4) 24
23 · 3
4 solvable, semiabelian 383
12T12 1/2[3:2]cD(4) 24
23 · 3
2 solvable, semiabelian 377
12T13 1/2[3:2]eD(4) 24
23 · 3
2 solvable, semiabelian 407
12T14 D(4)[x]C(3) 24
23 · 3
6 nilpotent, semiabelian 484
12T15 1/2[3:2]dD(4) 24
23 · 3
2 solvable, semiabelian 411
12T16 [32]E(4) 36
22 · 32
1 solvable, semiabelian, even 356
12T17 [32]4 36
22 · 32
1 solvable, semiabelian 202
12T18 [32]E(4) 36
22 · 32
6 solvable, semiabelian, even 358
12T19 [32]4 36
22 · 32
6 solvable, semiabelian 268
12T20 A(4)[x]C(3) 36
22 · 32
3 solvable, semiabelian, even 189
12T21 1/2[1/4.26]S(3) 48
24 · 3
2 solvable, semiabelian, even 888
12T22 S4(12d)x2 48
24 · 3
2 solvable, semiabelian 808
12T23 S4(6d)[x]2=[1/8.26]S(3) 48
24 · 3
2 solvable, semiabelian, even 1252
12T24 S4(6c)[x]2 48
24 · 3
2 solvable, semiabelian, even 1242
12T25 2A4(6)[x]2=[1/4.26]3 48
24 · 3
4 solvable, semiabelian, even 777
12T26 A4(12)x22 48
24 · 3
4 solvable, semiabelian, even 472
12T27 [2]S4(6)2 48
24 · 3
2 solvable, semiabelian 344
12T28 D(4)[x]S(3) 48
24 · 3
2 solvable, semiabelian 1079
12T29 [1/2.42]3 48
24 · 3
4 solvable, semiabelian 289
12T30 1/2[1/4.43]S(3) 48
24 · 3
2 solvable, semiabelian 375
12T31 [42]3 48
24 · 3
1 solvable, semiabelian, even 123
12T32 [E(4)2]3 48
24 · 3
1 solvable, semiabelian, even 386
12T33 A5(12) 60
22 · 3 · 5
1 not solvable, simple, irreducible, even 109
12T34 F36:2(12e) 72
23 · 32
1 solvable, semiabelian, even 599
12T35 [D62]2=D6wr2 72
23 · 32
1 solvable, semiabelian 595
12T36 F36:2(12d) 72
23 · 32
1 solvable, semiabelian 613
12T37 [32:2]E(4) 72
23 · 32
2 solvable, semiabelian, even 642
12T38 1/2[32:2]cD(4) 72
23 · 32
2 solvable, semiabelian 378
12T39 [32:2]4 72
23 · 32
2 solvable, semiabelian 324
12T40 F36(6)[x]2 72
23 · 32
2 solvable, semiabelian, even 368
12T41 1/2[(1/4.23)2]F36(6) 72
23 · 32
2 solvable, semiabelian 388
12T42 [32]D(4)=6wr2 72
23 · 32
6 solvable, semiabelian 464
12T43 A(4)[x]S(3) 72
23 · 32
1 solvable, semiabelian, even 434
12T44 1/2[3:2]S(4) 72
23 · 32
1 solvable, semiabelian 313
12T45 S(4)[x]C(3) 72
23 · 32
3 solvable, semiabelian 381
12T46 [(1/3.33):2]44 72
23 · 32
1 solvable, semiabelian, even 152
12T47 [(1/3.33):2]E(4)4 72
23 · 32
1 solvable, semiabelian, even 178
12T48 2S4(6)[x]2=[1/4.26]S(3) 96
25 · 3
4 solvable, semiabelian, even 1753
12T49 [2]2S4(6)2 96
25 · 3
2 solvable, semiabelian 738
12T50 1/2e[1/16.D(4)3]S(3) 96
25 · 3
2 solvable, semiabelian 727
12T51 [1/16.D(4)3]3 96
25 · 3
2 solvable, semiabelian 726
12T52 1/2c[1/16.D(4)3]S(3) 96
25 · 3
2 solvable, semiabelian 709
12T53 [1/2.42]S(3) 96
25 · 3
4 solvable, semiabelian 599
12T54 [(1/2.22)3]D(6)4 96
25 · 3
2 solvable, semiabelian 419
12T55 [1/2.43]3 96
25 · 3
2 solvable, semiabelian, even 430
12T56 [1/2.26]3 96
25 · 3
2 solvable, semiabelian, even 1416
12T57 [(1/2.22)3]A4(6)4 96
25 · 3
2 solvable, irreducible, even 246
12T58 [24]6 96
25 · 3
1 solvable, semiabelian, even 482
12T59 [23]A4(6) 96
25 · 3
1 solvable, semiabelian 514
12T60 [1/2[1/2.22]3]2A4(6)4 96
25 · 3
1 solvable, semiabelian, even 273
12T61 [23]A4(6)4 96
25 · 3
1 solvable, semiabelian 277
12T62 [42]S(3) 96
25 · 3
1 solvable, semiabelian, even 254
12T63 [1/2[1/2.22]3]S4(6d)8b 96
25 · 3
1 solvable, semiabelian, even 202
12T64 [1/2[1/2.22]3]S4(6d)8a 96
25 · 3
1 solvable, semiabelian 198
12T65 [1/2[1/2.22]3]S4(6c)4 96
25 · 3
1 solvable, semiabelian, even 184
12T66 [1/2[1/2.22]3]S4(6d)2 96
25 · 3
1 solvable, semiabelian 628
12T67 [E(4)2]S(3) 96
25 · 3
1 solvable, semiabelian, even 399
12T68 [1/2[1/2.22]3]S4(6c) 96
25 · 3
1 solvable, semiabelian, even 579
12T69 [24]D6(6) 96
25 · 3
1 solvable, semiabelian, even 445
12T70 1/2[33:2]E(4) 108
22 · 33
3 solvable, semiabelian, even 459
12T71 [33]E(4) 108
22 · 33
1 solvable, semiabelian, even 300
12T72 [33]4 108
22 · 33
1 solvable, semiabelian 285
12T73 1/2[33:2]4 108
22 · 33
3 solvable, semiabelian 261
12T74 S5(12) 120
23 · 3 · 5
1 not solvable, irreducible, even 260
12T75 L(6)[x]2 120
23 · 3 · 5
2 not solvable, even 327
12T76 [2]L(6)6 120
23 · 3 · 5
2 not solvable, even 372
12T77 [S(3)2]E(4) 144
24 · 32
2 solvable, semiabelian, even 1027
12T78 [2]F36:22{S32} 144
24 · 32
2 solvable, semiabelian 966
12T79 [S(3)2]4 144
24 · 32
2 solvable, semiabelian 567
12T80 [2]F36:22{32:4} 144
24 · 32
2 solvable, semiabelian 612
12T81 [32:2]D(4) 144
24 · 32
2 solvable, semiabelian 706
12T82 [(1/4.23)2]F36(6) 144
24 · 32
2 solvable, semiabelian 590
12T83 S(4)[x]S(3) 144
24 · 32
1 solvable, semiabelian 551
12T84 [(1/3.33):2]D(4)4 144
24 · 32
1 solvable, semiabelian, even 288
12T85 [1/4E(4)3:3]3 144
24 · 32
1 solvable, semiabelian, even 238
12T86 [1/16.D(4)3]S(3) 192
26 · 3
2 solvable, semiabelian 1521
12T87 [25]6 192
26 · 3
2 solvable, semiabelian, even 901
12T88 [24]A4(6) 192
26 · 3
2 solvable, semiabelian 913
12T89 [(1/2.22)3]2A4(6)4{n4} 192
26 · 3
2 solvable, semiabelian, even 480
12T90 [E(4)3]3=E(4)wr3 192
26 · 3
4 solvable, semiabelian, even 1117
12T91 [(1/2.22)3]2A4(6)4{n2} 192
26 · 3
2 solvable, even 404
12T92 [24]A4(6)4{n4} 192
26 · 3
2 solvable, semiabelian 496
12T93 [24]A4(6)4{n2} 192
26 · 3
2 solvable 421
12T94 [43]3=4wr3 192
26 · 3
4 solvable, semiabelian 369
12T95 [1/2.43]S(3) 192
26 · 3
2 solvable, semiabelian, even 523
12T96 [(1/2.22)3]S4(6d)8 192
26 · 3
2 solvable, semiabelian 397
12T97 [(1/2.22)3]S4(6c)4 192
26 · 3
2 solvable, semiabelian, even 381
12T98 1/2[43]S(3) 192
26 · 3
2 solvable, semiabelian 226
12T99 [(1/2.22)3]2A4(6)2 192
26 · 3
2 solvable, semiabelian 438
12T100 [(1/2.22)3]S4(6d)2 192
26 · 3
2 solvable, semiabelian 1173
12T101 [1/2.26]S(3) 192
26 · 3
2 solvable, semiabelian, even 1505
12T102 [(1/2.22)3]S4(6c)2 192
26 · 3
2 solvable, semiabelian 624
12T103 1/2[E(4)3]S(3) 192
26 · 3
2 solvable, semiabelian, even 1270
12T104 [(1/2.22)3]2A4(6)8 192
26 · 3
2 solvable 377
12T105 1/2[26]6 192
26 · 3
2 solvable, semiabelian 717
12T106 [25]D6(6) 192
26 · 3
2 solvable, semiabelian, even 804
12T107 1/2[26]D6 192
26 · 3
2 solvable, semiabelian 560
12T108 1/2[25]D(6) 192
26 · 3
1 solvable, semiabelian, even 905
12T109 [24]D(6) 192
26 · 3
1 solvable, semiabelian, even 869
12T110 [23]S4(6d) 192
26 · 3
1 solvable, semiabelian 821
12T111 [23]S4(6)2 192
26 · 3
1 solvable, semiabelian 863
12T112 [1/2[1/2.22]3]2S4(6)8 192
26 · 3
1 solvable, semiabelian, even 501
12T113 [1/2[1/2.22]3]2S4(6)4 192
26 · 3
1 solvable, semiabelian, even 595
12T114 [23]S4(6)4 192
26 · 3
1 solvable, semiabelian 587
12T115 [23]S4(6)8 192
26 · 3
1 solvable, semiabelian 587
12T116 [33]D(4) 216
23 · 33
1 solvable, semiabelian 614
12T117 [33:2]E(4) 216
23 · 33
1 solvable, semiabelian, even 529
12T118 1/2[33:2]eD(4) 216
23 · 33
1 solvable, semiabelian 488
12T119 [33:2]4 216
23 · 33
1 solvable, semiabelian 393
12T120 1/2[33:2]cD(4) 216
23 · 33
1 solvable, semiabelian 638
12T121 1/2[33:2]dD(4) 216
23 · 33
3 solvable, semiabelian 654
12T122 [(1/3.33):2]A(4)4 216
23 · 33
1 solvable, even 132
12T123 L(6):2[x]2 240
24 · 3 · 5
2 not solvable, even 666
12T124 [2]L(6):212 240
24 · 3 · 5
2 not solvable, irreducible 293
12T125 [S(3)2]D(4)=D(6)wr2 288
25 · 32
2 solvable, semiabelian 1421
12T126 [A42]2=A4wr2 288
25 · 32
1 solvable, semiabelian, even 399
12T127 [1/4E(4)3:3]S(3)2 288
25 · 32
1 solvable, semiabelian 389
12T128 [1/4E(4)3:3]S(3) 288
25 · 32
1 solvable, semiabelian, even 380
12T129 [1/4E(4)3:3:2]3 288
25 · 32
1 solvable, semiabelian 375
12T130 [34]E(4)=3wrE(4) 324
22 · 34
3 solvable, semiabelian, even 275
12T131 [34]4=3wr4 324
22 · 34
3 solvable, semiabelian 238
12T132 1/3[34]A(4) 324
22 · 34
1 solvable, semiabelian, even 268
12T133 [33]A(4) 324
22 · 34
1 solvable, semiabelian, even 270
12T134 [26]6=2wr6 384
27 · 3
2 solvable, semiabelian 1588
12T135 [26]D6=2wrD6(6) 384
27 · 3
2 solvable, semiabelian 1261
12T136 [25]D(6) 384
27 · 3
2 solvable, semiabelian, even 1524
12T137 [24]S4(6d) 384
27 · 3
2 solvable, semiabelian 1406
12T138 [(1/2.22)3]2S4(6)4 384
27 · 3
2 solvable, semiabelian, even 959
12T139 [E(4)3]S(3)=E(4)wrS(3) 384
27 · 3
4 solvable, semiabelian, even 1202
12T140 [24]S4(6d)4 384
27 · 3
2 solvable, semiabelian 992
12T141 [1/4.cD(4)3]3 384
27 · 3
2 solvable, semiabelian 736
12T142 [1/4.eD(4)3]3 384
27 · 3
2 solvable, semiabelian 1521
12T143 [24]2A4(6)4 384
27 · 3
2 solvable 670
12T144 [25]A4(6) 384
27 · 3
2 solvable, semiabelian, even 985
12T145 1/2[26]D(6) 384
27 · 3
2 solvable, semiabelian 726
12T146 [24]S4(6c) 384
27 · 3
2 solvable, semiabelian 840
12T147 [(1/2.22)3]2S4(6)8 384
27 · 3
2 solvable, semiabelian 558
12T148 1/2[1/4.eD(4)3]S(3) 384
27 · 3
2 solvable, semiabelian 1257
12T149 [24]S4(6c)4 384
27 · 3
2 solvable, semiabelian 699
12T150 [43]S(3)=4wrS(3) 384
27 · 3
4 solvable, semiabelian 459
12T151 1/2[1/4.cD(4)3]S(3) 384
27 · 3
2 solvable, semiabelian 440
12T152 [(1/2.22)3]2S4(6)2{S4(6c)} 384
27 · 3
2 solvable, semiabelian 763
12T153 [(1/2.22)3]2S4(6)2{S4(6d)} 384
27 · 3
2 solvable, semiabelian 817
12T154 [25]D(6)2t 384
27 · 3
2 solvable, semiabelian 744
12T155 [25]D(6)2i 384
27 · 3
2 solvable, semiabelian 1129
12T156 [33:2]D(4) 432
24 · 33
1 solvable, semiabelian 1013
12T157 [(1/3.33):2]S(4)4 432
24 · 33
1 solvable, even 213
12T158 [25]F18(6) 576
26 · 32
2 solvable, semiabelian, even 671
12T159 [25]F18(6)2 576
26 · 32
2 solvable, semiabelian 556
12T160 1/2[S4(6c)2]2 576
26 · 32
1 solvable, semiabelian 310
12T161 [1/2.S4(6c)2]2 576
26 · 32
1 solvable, semiabelian, even 493
12T162 [24]F36(6) 576
26 · 32
1 solvable, semiabelian, even 391
12T163 [24]F18(6):2 576
26 · 32
1 solvable, semiabelian, even 516
12T164 [1/9.A(4)3]3 576
26 · 32
1 solvable, semiabelian, even 502
12T165 [1/4E(4)3:3:2]3 576
26 · 32
1 solvable, semiabelian 593
12T166 [1/9.A(4)3]33 576
26 · 32
1 solvable, semiabelian, even 335
12T167 [34]D(4)=3wrD(4) 648
23 · 34
3 solvable, semiabelian 545
12T168 [34:2]E(4) 648
23 · 34
1 solvable, semiabelian, even 388
12T169 1/2[34:2]cD(4) 648
23 · 34
1 solvable, semiabelian 454
12T170 [34:2]4 648
23 · 34
1 solvable, semiabelian 427
12T171 [34:2]E(4)2 648
23 · 34
1 solvable, semiabelian, even 298
12T172 1/2[34:22]E(4) 648
23 · 34
1 solvable, semiabelian, even 460
12T173 [34:2]44 648
23 · 34
1 solvable, semiabelian, even 205
12T174 [34:2]E(4)4 648
23 · 34
1 solvable, semiabelian, even 185
12T175 [33]S(4) 648
23 · 34
1 solvable, semiabelian 396
12T176 [33:2]A(4) 648
23 · 34
1 solvable, semiabelian, even 553
12T177 [33]S(4)6 648
23 · 34
1 solvable, semiabelian 506
12T178 1/2[33:2]S(4) 648
23 · 34
1 solvable, semiabelian 461
12T179 L(2,11) 660
22 · 3 · 5 · 11
1 not solvable, primitive, simple, irreducible, even 36
12T180 A(6)[x]2 720
24 · 32 · 5
2 not solvable, even 335
12T181 M10(12)=[A6[1/360]{M10}A6]22 720
24 · 32 · 5
1 not solvable, irreducible, even 22
12T182 PGL(2,9)(12)=[A6[1/360]{M10}A6]2 720
24 · 32 · 5
1 not solvable, irreducible, even 71
12T183 S6(12) 720
24 · 32 · 5
1 not solvable, irreducible, even 372
12T184 [25]S4(6d) 768
28 · 3
2 solvable, semiabelian, even 1166
12T185 [1/4.cD(4)3]S(3) 768
28 · 3
2 solvable, semiabelian 1290
12T186 [1/4.eD(4)3]S(3) 768
28 · 3
2 solvable, semiabelian 1987
12T187 [25]2A4(6) 768
28 · 3
2 solvable, semiabelian, even 1637
12T188 [26]A4=2wrA4(6) 768
28 · 3
2 solvable, semiabelian 1802
12T189 [1/2.cD(4)3]3 768
28 · 3
2 solvable, semiabelian 1131
12T190 1/2[26]S4(6d) 768
28 · 3
2 solvable, semiabelian 1125
12T191 [25]S4(6c) 768
28 · 3
2 solvable, semiabelian, even 984
12T192 1/2[26]S4(6c) 768
28 · 3
2 solvable, semiabelian 833
12T193 [26]D(6)=2wrD(6) 768
28 · 3
2 solvable, semiabelian 2205
12T194 [34]A(4)=3wrA(4) 972
22 · 35
3 solvable, semiabelian, even 228
12T195 [25]F18(6):2 1152
27 · 32
2 solvable, semiabelian, even 1063
12T196 [25]F18:22 1152
27 · 32
2 solvable, semiabelian 432
12T197 1/2[26]F18:2 1152
27 · 32
2 solvable, semiabelian 775
12T198 1/2[26]F36 1152
27 · 32
2 solvable, semiabelian 717
12T199 [25]F36(6) 1152
27 · 32
2 solvable, semiabelian, even 869
12T200 [S4(6c)2]2=S4(6c)wr2 1152
27 · 32
1 solvable, semiabelian 701
12T201 [24]F36:24 1152
27 · 32
1 solvable, semiabelian 1039
12T202 [24]F36:22 1152
27 · 32
1 solvable, semiabelian, even 1208
12T203 [S4(6d)2]2=S4(6d)wr2 1152
27 · 32
1 solvable, semiabelian, even 849
12T204 [1/9.A(4)3]S(3)2 1152
27 · 32
1 solvable, semiabelian 513
12T205 [E(4)3:3:2]3 1152
27 · 32
1 solvable, semiabelian 544
12T206 [1/9.A(4)3]S(3) 1152
27 · 32
1 solvable, semiabelian, even 826
12T207 [1/9.A(4)3]S(3)6 1152
27 · 32
1 solvable, semiabelian 482
12T208 [2A42]2=2A4wr2=2wrF18(6) 1152
27 · 32
2 solvable, semiabelian 1267
12T209 1/2[34:22]cD(4) 1296
24 · 34
1 solvable, semiabelian 654
12T210 [34:22]E(4) 1296
24 · 34
1 solvable, semiabelian, even 729
12T211 [34:22]4 1296
24 · 34
1 solvable, semiabelian 497
12T212 [34:2]D(4)8 1296
24 · 34
1 solvable, semiabelian, even 277
12T213 [33:2]S(4) 1296
24 · 34
1 solvable, semiabelian 739
12T214 [1/2.F362]2 1296
24 · 34
1 solvable, semiabelian, even 372
12T215 1/2[F362]2 1296
24 · 34
1 solvable, semiabelian, even 229
12T216 [34:2]D(4)4 1296
24 · 34
1 solvable, semiabelian, even 427
12T217 [34:2]D(4) 1296
24 · 34
1 solvable, semiabelian 881
12T218 PGL(2,11) 1320
23 · 3 · 5 · 11
1 not solvable, primitive, irreducible 122
12T219 S(6)[x]2 1440
25 · 32 · 5
2 not solvable, even 970
12T220 M10.2(12)=A6.E4(12)=[S6[1/720]{M10}S6]2 1440
25 · 32 · 5
1 not solvable, irreducible, even 176
12T221 [1/2.cD(4)3]S(3) 1536
29 · 3
2 solvable, semiabelian 1237
12T222 [D(4)4]3=D(4)wr3 1536
29 · 3
2 solvable, semiabelian 2621
12T223 1/2e[D(4)3]S(3) 1536
29 · 3
2 solvable, semiabelian 1455
12T224 [26]S4(6c)=2wrS4(6c) 1536
29 · 3
2 solvable, semiabelian 1584
12T225 1/2c[D(4)3]S(3) 1536
29 · 3
2 solvable, semiabelian 1203
12T226 [25]2S4(6) 1536
29 · 3
2 solvable, semiabelian, even 1837
12T227 [26]S4(6d)=2wrS4(6d) 1536
29 · 3
2 solvable, semiabelian 2061
12T228 1/3[A(4)3]3 1728
26 · 33
1 solvable, semiabelian, even 192
12T229 [1/3.A(4)3]3 1728
26 · 33
1 solvable, semiabelian, even 316
12T230 [25]L(6) 1920
27 · 3 · 5
2 not solvable, even 704
12T231 [34]S(4)=3wrS(4) 1944
23 · 35
3 solvable, semiabelian 332
12T232 [34:2]A(4)4 1944
23 · 35
1 solvable, even 228
12T233 1/2[34:2]S(4) 1944
23 · 35
1 solvable, semiabelian 373
12T234 [34:2]A(4) 1944
23 · 35
1 solvable, semiabelian, even 415
12T235 [25]F36:22{S32,t} 2304
28 · 32
2 solvable, semiabelian 1803
12T236 [25]F36(6):2 2304
28 · 32
2 solvable, semiabelian, even 1813
12T237 [25]F36:22{S32,i} 2304
28 · 32
2 solvable, semiabelian 1698
12T238 [25]F36:22{32:4} 2304
28 · 32
2 solvable, semiabelian 1666
12T239 [E(4)3:3:2]3 2304
28 · 32
1 solvable, semiabelian 938
12T240 [26]F18:2=2wrF18(6):2 2304
28 · 32
2 solvable, semiabelian 1796
12T241 [26]F36=2wrF36(6) 2304
28 · 32
2 solvable, semiabelian 1632
12T242 [34:23]E(4) 2592
25 · 34
1 solvable, semiabelian, even 380
12T243 [34:22]D(4)4 2592
25 · 34
1 solvable, semiabelian, even 393
12T244 1/2[S(3)4]4 2592
25 · 34
1 solvable, semiabelian, even 382
12T245 [34:23]4 2592
25 · 34
1 solvable, semiabelian 345
12T246 1/2[S(3)4]E(4) 2592
25 · 34
1 solvable, semiabelian 331
12T247 [34:22]D(4)2 2592
25 · 34
1 solvable, semiabelian 433
12T248 [34:22]D(4) 2592
25 · 34
1 solvable, semiabelian 807
12T249 [F362]2=F36wr2 2592
25 · 34
1 solvable, semiabelian, even 313
12T250 [D(4)4]S(3)=D(4)wrS(3) 3072
210 · 3
2 solvable, semiabelian 3157
12T251 [1/3.A(4)3]S(3)2 3456
27 · 33
1 solvable, semiabelian 513
12T252 [1/3.A(4)3]S(3) 3456
27 · 33
1 solvable, semiabelian, even 681
12T253 [E(4)3:32:2]3 3456
27 · 33
1 solvable, semiabelian 553
12T254 [1/3.A(4)3]S(3)6 3456
27 · 33
1 solvable, semiabelian 329
12T255 [26]L(6)=2wrL(6) 3840
28 · 3 · 5
2 not solvable 1302
12T256 1/2[26]L(6):2 3840
28 · 3 · 5
2 not solvable 638
12T257 [25]L(6):2 3840
28 · 3 · 5
2 not solvable, even 662
12T258 [34:2]S(4) 3888
24 · 35
1 solvable, semiabelian 645
12T259 [34:2]S(4)8 3888
24 · 35
1 solvable, even 253
12T260 [2S42]2=2S4wr2 4608
29 · 32
2 solvable, semiabelian 2762
12T261 [S(3)4]E(4)=S(3)wrE(4) 5184
26 · 34
1 solvable, semiabelian 453
12T262 1/2[S(3)4]dD(4) 5184
26 · 34
1 solvable, semiabelian 481
12T263 1/2[S(3)4]cD(4) 5184
26 · 34
1 solvable, semiabelian 444
12T264 [S(3)4]4=S(3)wr4 5184
26 · 34
1 solvable, semiabelian 624
12T265 [A(4)3]3=A(4)wr3 5184
26 · 34
1 solvable, semiabelian, even 312
12T266 1/2[S(3)4]eD(4) 5184
26 · 34
1 solvable, semiabelian, even 541
12T267 [34:23]D(4) 5184
26 · 34
1 solvable, semiabelian 708
12T268 [E(4)3:32:2]S(3) 6912
28 · 33
1 solvable, semiabelian 925
12T269 [L(6)2]2=L(6)wr2 7200
25 · 32 · 52
1 not solvable, irreducible, even 298
12T270 [26]L(6):2=2wrL(6):2 7680
29 · 3 · 5
2 not solvable 1345
12T271 [34:23]A(4) 7776
25 · 35
1 solvable, semiabelian, even 269
12T272 M11(12) 7920
24 · 32 · 5 · 11
1 not solvable, primitive, simple, irreducible, even 42
12T273 [1/4.S(4)3]3 10368
27 · 34
1 solvable, semiabelian 390
12T274 [S(3)4]D(4)=S(3)wrD(4) 10368
27 · 34
1 solvable, semiabelian 1065
12T275 [A(4)3]S(3)=A(4)wrS(3) 10368
27 · 34
1 solvable, semiabelian, even 489
12T276 1/2[1/4.S(4)3]S(3) 10368
27 · 34
1 solvable, semiabelian 328
12T277 [25]A(6) 11520
28 · 32 · 5
2 not solvable, even 524
12T278 1/2[(L(6):2)2]2 14400
26 · 32 · 52
1 not solvable, irreducible 154
12T279 [1/2.(L(6):2)2]2 14400
26 · 32 · 52
1 not solvable, irreducible, even 367
12T280 [S(3)4]A(4)=S(3)wrA(4) 15552
26 · 35
1 solvable, semiabelian 418
12T281 [34:23]S(4) 15552
26 · 35
1 solvable, semiabelian 348
12T282 1/2[S(3)4]S(4) 15552
26 · 35
1 solvable, even 296
12T283 [1/4.S(4)3]S(3) 20736
28 · 34
1 solvable, semiabelian 629
12T284 [1/2.S(4)3]3 20736
28 · 34
1 solvable, semiabelian, even 459
12T285 [25]S(6) 23040
29 · 32 · 5
2 not solvable, even 1559
12T286 [26]A(6)=2wrA(6) 23040
29 · 32 · 5
2 not solvable 1059
12T287 1/2[26]S(6) 23040
29 · 32 · 5
2 not solvable, irreducible 790
12T288 [(L(6):2)2]2=L(6):2wr2 28800
27 · 32 · 52
1 not solvable, irreducible 358
12T289 [S(3)4]S(4)=S(3)wrS(4) 31104
27 · 35
1 solvable, semiabelian 835
12T290 [1/2.S(4)3]S(3) 41472
29 · 34
1 solvable, semiabelian, even 662
12T291 1/2[S(4)3]S(3) 41472
29 · 34
1 solvable, semiabelian 539
12T292 [S(4)3]3=S(4)wr3 41472
29 · 34
1 solvable, semiabelian 1217
12T293 [26]S(6)=2wrS(6) 46080
210 · 32 · 5
2 not solvable 2477
12T294 [S(4)3]S(3)=S(4)wrS(3) 82944
210 · 34
1 solvable, semiabelian 1236
12T295 M(12) 95040
26 · 33 · 5 · 11
1 not solvable, primitive, simple, irreducible, even 66
12T296 [A(6)2]2=A(6)wr2 259200
27 · 34 · 52
1 not solvable, irreducible, even 453
12T297 [1/2.S(6)2]2 518400
28 · 34 · 52
1 not solvable, irreducible, even 702
12T298 1/2[S(6)2]2 518400
28 · 34 · 52
1 not solvable, irreducible 253
12T299 [S(6)2]2=S(6)wr2 1036800
29 · 34 · 52
1 not solvable, irreducible 1237
12T300 A(12) 239500800
29 · 35 · 52 · 7 · 11
1 not solvable, primitive, simple, irreducible, even 124
12T301 S(12) 479001600
210 · 35 · 52 · 7 · 11
1 not solvable, primitive, irreducible 417

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