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Transitive Groups of degree 12

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Transitive Groups of degree 12
G Name |G| |G| fact. |Z(G)| Properties of G # fields
12T1 C(4)[x]C(3) 12
22 · 3
12 cyclic, semiabelian 192
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 622
12T4 A4(12) 12
22 · 3
1 solvable, semiabelian, even 208
12T5 1/2[3:2]4 12
22 · 3
2 solvable, semiabelian 186
12T6 A4(12)x2 24
23 · 3
2 solvable, semiabelian, even 507
12T7 A4(6)[x]2=[1/8.26]3 24
23 · 3
2 solvable, semiabelian, even 463
12T8 S4(12d) 24
23 · 3
1 solvable, semiabelian 527
12T9 1/2[1/8.26]S(3)=S4(12e) 24
23 · 3
1 solvable, semiabelian, even 505
12T10 S(3)[x]E(4) 24
23 · 3
4 solvable, semiabelian, even 785
12T11 S(3)[x]C(4) 24
23 · 3
4 solvable, semiabelian 365
12T12 1/2[3:2]cD(4) 24
23 · 3
2 solvable, semiabelian 368
12T13 1/2[3:2]eD(4) 24
23 · 3
2 solvable, semiabelian 397
12T14 D(4)[x]C(3) 24
23 · 3
6 nilpotent, semiabelian 481
12T15 1/2[3:2]dD(4) 24
23 · 3
2 solvable, semiabelian 403
12T16 [32]E(4) 36
22 · 32
1 solvable, semiabelian, even 352
12T17 [32]4 36
22 · 32
1 solvable, semiabelian 192
12T18 [32]E(4) 36
22 · 32
6 solvable, semiabelian, even 357
12T19 [32]4 36
22 · 32
6 solvable, semiabelian 266
12T20 A(4)[x]C(3) 36
22 · 32
3 solvable, semiabelian, even 188
12T21 1/2[1/4.26]S(3) 48
24 · 3
2 solvable, semiabelian, even 877
12T22 S4(12d)x2 48
24 · 3
2 solvable, semiabelian 807
12T23 S4(6d)[x]2=[1/8.26]S(3) 48
24 · 3
2 solvable, semiabelian, even 1249
12T24 S4(6c)[x]2 48
24 · 3
2 solvable, semiabelian, even 1241
12T25 2A4(6)[x]2=[1/4.26]3 48
24 · 3
4 solvable, semiabelian, even 753
12T26 A4(12)x22 48
24 · 3
4 solvable, semiabelian, even 453
12T27 [2]S4(6)2 48
24 · 3
2 solvable, semiabelian 322
12T28 D(4)[x]S(3) 48
24 · 3
2 solvable, semiabelian 1053
12T29 [1/2.42]3 48
24 · 3
4 solvable, semiabelian 262
12T30 1/2[1/4.43]S(3) 48
24 · 3
2 solvable, semiabelian 334
12T31 [42]3 48
24 · 3
1 solvable, semiabelian, even 123
12T32 [E(4)2]3 48
24 · 3
1 solvable, semiabelian, even 383
12T33 A5(12) 60
22 · 3 · 5
1 not solvable, simple, irreducible, even 96
12T34 F36:2(12e) 72
23 · 32
1 solvable, semiabelian, even 595
12T35 [D62]2=D6wr2 72
23 · 32
1 solvable, semiabelian 579
12T36 F36:2(12d) 72
23 · 32
1 solvable, semiabelian 613
12T37 [32:2]E(4) 72
23 · 32
2 solvable, semiabelian, even 617
12T38 1/2[32:2]cD(4) 72
23 · 32
2 solvable, semiabelian 370
12T39 [32:2]4 72
23 · 32
2 solvable, semiabelian 323
12T40 F36(6)[x]2 72
23 · 32
2 solvable, semiabelian, even 367
12T41 1/2[(1/4.23)2]F36(6) 72
23 · 32
2 solvable, semiabelian 385
12T42 [32]D(4)=6wr2 72
23 · 32
6 solvable, semiabelian 461
12T43 A(4)[x]S(3) 72
23 · 32
1 solvable, semiabelian, even 421
12T44 1/2[3:2]S(4) 72
23 · 32
1 solvable, semiabelian 301
12T45 S(4)[x]C(3) 72
23 · 32
3 solvable, semiabelian 375
12T46 [(1/3.33):2]44 72
23 · 32
1 solvable, semiabelian, even 151
12T47 [(1/3.33):2]E(4)4 72
23 · 32
1 solvable, semiabelian, even 177
12T48 2S4(6)[x]2=[1/4.26]S(3) 96
25 · 3
4 solvable, semiabelian, even 1736
12T49 [2]2S4(6)2 96
25 · 3
2 solvable, semiabelian 712
12T50 1/2e[1/16.D(4)3]S(3) 96
25 · 3
2 solvable, semiabelian 690
12T51 [1/16.D(4)3]3 96
25 · 3
2 solvable, semiabelian 645
12T52 1/2c[1/16.D(4)3]S(3) 96
25 · 3
2 solvable, semiabelian 656
12T53 [1/2.42]S(3) 96
25 · 3
4 solvable, semiabelian 581
12T54 [(1/2.22)3]D(6)4 96
25 · 3
2 solvable, semiabelian 412
12T55 [1/2.43]3 96
25 · 3
2 solvable, semiabelian, even 428
12T56 [1/2.26]3 96
25 · 3
2 solvable, semiabelian, even 1377
12T57 [(1/2.22)3]A4(6)4 96
25 · 3
2 solvable, irreducible, even 237
12T58 [24]6 96
25 · 3
1 solvable, semiabelian, even 436
12T59 [23]A4(6) 96
25 · 3
1 solvable, semiabelian 486
12T60 [1/2[1/2.22]3]2A4(6)4 96
25 · 3
1 solvable, semiabelian, even 265
12T61 [23]A4(6)4 96
25 · 3
1 solvable, semiabelian 253
12T62 [42]S(3) 96
25 · 3
1 solvable, semiabelian, even 224
12T63 [1/2[1/2.22]3]S4(6d)8b 96
25 · 3
1 solvable, semiabelian, even 190
12T64 [1/2[1/2.22]3]S4(6d)8a 96
25 · 3
1 solvable, semiabelian 189
12T65 [1/2[1/2.22]3]S4(6c)4 96
25 · 3
1 solvable, semiabelian, even 179
12T66 [1/2[1/2.22]3]S4(6d)2 96
25 · 3
1 solvable, semiabelian 620
12T67 [E(4)2]S(3) 96
25 · 3
1 solvable, semiabelian, even 389
12T68 [1/2[1/2.22]3]S4(6c) 96
25 · 3
1 solvable, semiabelian, even 578
12T69 [24]D6(6) 96
25 · 3
1 solvable, semiabelian, even 440
12T70 1/2[33:2]E(4) 108
22 · 33
3 solvable, semiabelian, even 456
12T71 [33]E(4) 108
22 · 33
1 solvable, semiabelian, even 295
12T72 [33]4 108
22 · 33
1 solvable, semiabelian 283
12T73 1/2[33:2]4 108
22 · 33
3 solvable, semiabelian 259
12T74 S5(12) 120
23 · 3 · 5
1 not solvable, irreducible, even 226
12T75 L(6)[x]2 120
23 · 3 · 5
2 not solvable, even 303
12T76 [2]L(6)6 120
23 · 3 · 5
2 not solvable, even 340
12T77 [S(3)2]E(4) 144
24 · 32
2 solvable, semiabelian, even 967
12T78 [2]F36:22{S32} 144
24 · 32
2 solvable, semiabelian 930
12T79 [S(3)2]4 144
24 · 32
2 solvable, semiabelian 550
12T80 [2]F36:22{32:4} 144
24 · 32
2 solvable, semiabelian 602
12T81 [32:2]D(4) 144
24 · 32
2 solvable, semiabelian 684
12T82 [(1/4.23)2]F36(6) 144
24 · 32
2 solvable, semiabelian 589
12T83 S(4)[x]S(3) 144
24 · 32
1 solvable, semiabelian 529
12T84 [(1/3.33):2]D(4)4 144
24 · 32
1 solvable, semiabelian, even 285
12T85 [1/4E(4)3:3]3 144
24 · 32
1 solvable, semiabelian, even 233
12T86 [1/16.D(4)3]S(3) 192
26 · 3
2 solvable, semiabelian 1477
12T87 [25]6 192
26 · 3
2 solvable, semiabelian, even 813
12T88 [24]A4(6) 192
26 · 3
2 solvable, semiabelian 881
12T89 [(1/2.22)3]2A4(6)4{n4} 192
26 · 3
2 solvable, semiabelian, even 455
12T90 [E(4)3]3=E(4)wr3 192
26 · 3
4 solvable, semiabelian, even 1076
12T91 [(1/2.22)3]2A4(6)4{n2} 192
26 · 3
2 solvable, even 384
12T92 [24]A4(6)4{n4} 192
26 · 3
2 solvable, semiabelian 491
12T93 [24]A4(6)4{n2} 192
26 · 3
2 solvable 393
12T94 [43]3=4wr3 192
26 · 3
4 solvable, semiabelian 358
12T95 [1/2.43]S(3) 192
26 · 3
2 solvable, semiabelian, even 480
12T96 [(1/2.22)3]S4(6d)8 192
26 · 3
2 solvable, semiabelian 338
12T97 [(1/2.22)3]S4(6c)4 192
26 · 3
2 solvable, semiabelian, even 357
12T98 1/2[43]S(3) 192
26 · 3
2 solvable, semiabelian 219
12T99 [(1/2.22)3]2A4(6)2 192
26 · 3
2 solvable, semiabelian 412
12T100 [(1/2.22)3]S4(6d)2 192
26 · 3
2 solvable, semiabelian 1150
12T101 [1/2.26]S(3) 192
26 · 3
2 solvable, semiabelian, even 1475
12T102 [(1/2.22)3]S4(6c)2 192
26 · 3
2 solvable, semiabelian 545
12T103 1/2[E(4)3]S(3) 192
26 · 3
2 solvable, semiabelian, even 1244
12T104 [(1/2.22)3]2A4(6)8 192
26 · 3
2 solvable 363
12T105 1/2[26]6 192
26 · 3
2 solvable, semiabelian 611
12T106 [25]D6(6) 192
26 · 3
2 solvable, semiabelian, even 786
12T107 1/2[26]D6 192
26 · 3
2 solvable, semiabelian 419
12T108 1/2[25]D(6) 192
26 · 3
1 solvable, semiabelian, even 868
12T109 [24]D(6) 192
26 · 3
1 solvable, semiabelian, even 845
12T110 [23]S4(6d) 192
26 · 3
1 solvable, semiabelian 803
12T111 [23]S4(6)2 192
26 · 3
1 solvable, semiabelian 839
12T112 [1/2[1/2.22]3]2S4(6)8 192
26 · 3
1 solvable, semiabelian, even 464
12T113 [1/2[1/2.22]3]2S4(6)4 192
26 · 3
1 solvable, semiabelian, even 573
12T114 [23]S4(6)4 192
26 · 3
1 solvable, semiabelian 575
12T115 [23]S4(6)8 192
26 · 3
1 solvable, semiabelian 560
12T116 [33]D(4) 216
23 · 33
1 solvable, semiabelian 614
12T117 [33:2]E(4) 216
23 · 33
1 solvable, semiabelian, even 472
12T118 1/2[33:2]eD(4) 216
23 · 33
1 solvable, semiabelian 478
12T119 [33:2]4 216
23 · 33
1 solvable, semiabelian 391
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 651
12T122 [(1/3.33):2]A(4)4 216
23 · 33
1 solvable, even 86
12T123 L(6):2[x]2 240
24 · 3 · 5
2 not solvable, even 583
12T124 [2]L(6):212 240
24 · 3 · 5
2 not solvable, irreducible 215
12T125 [S(3)2]D(4)=D(6)wr2 288
25 · 32
2 solvable, semiabelian 1391
12T126 [A42]2=A4wr2 288
25 · 32
1 solvable, semiabelian, even 370
12T127 [1/4E(4)3:3]S(3)2 288
25 · 32
1 solvable, semiabelian 386
12T128 [1/4E(4)3:3]S(3) 288
25 · 32
1 solvable, semiabelian, even 361
12T129 [1/4E(4)3:3:2]3 288
25 · 32
1 solvable, semiabelian 359
12T130 [34]E(4)=3wrE(4) 324
22 · 34
3 solvable, semiabelian, even 255
12T131 [34]4=3wr4 324
22 · 34
3 solvable, semiabelian 222
12T132 1/3[34]A(4) 324
22 · 34
1 solvable, semiabelian, even 263
12T133 [33]A(4) 324
22 · 34
1 solvable, semiabelian, even 267
12T134 [26]6=2wr6 384
27 · 3
2 solvable, semiabelian 1355
12T135 [26]D6=2wrD6(6) 384
27 · 3
2 solvable, semiabelian 1078
12T136 [25]D(6) 384
27 · 3
2 solvable, semiabelian, even 1447
12T137 [24]S4(6d) 384
27 · 3
2 solvable, semiabelian 1386
12T138 [(1/2.22)3]2S4(6)4 384
27 · 3
2 solvable, semiabelian, even 885
12T139 [E(4)3]S(3)=E(4)wrS(3) 384
27 · 3
4 solvable, semiabelian, even 1186
12T140 [24]S4(6d)4 384
27 · 3
2 solvable, semiabelian 944
12T141 [1/4.cD(4)3]3 384
27 · 3
2 solvable, semiabelian 683
12T142 [1/4.eD(4)3]3 384
27 · 3
2 solvable, semiabelian 1385
12T143 [24]2A4(6)4 384
27 · 3
2 solvable 649
12T144 [25]A4(6) 384
27 · 3
2 solvable, even 843
12T145 1/2[26]D(6) 384
27 · 3
2 solvable, semiabelian 679
12T146 [24]S4(6c) 384
27 · 3
2 solvable, semiabelian 735
12T147 [(1/2.22)3]2S4(6)8 384
27 · 3
2 solvable, semiabelian 459
12T148 1/2[1/4.eD(4)3]S(3) 384
27 · 3
2 solvable, semiabelian 1207
12T149 [24]S4(6c)4 384
27 · 3
2 solvable, semiabelian 604
12T150 [43]S(3)=4wrS(3) 384
27 · 3
4 solvable, semiabelian 443
12T151 1/2[1/4.cD(4)3]S(3) 384
27 · 3
2 solvable, semiabelian 386
12T152 [(1/2.22)3]2S4(6)2{S4(6c)} 384
27 · 3
2 solvable, semiabelian 752
12T153 [(1/2.22)3]2S4(6)2{S4(6d)} 384
27 · 3
2 solvable, semiabelian 755
12T154 [25]D(6)2t 384
27 · 3
2 solvable, semiabelian 737
12T155 [25]D(6)2i 384
27 · 3
2 solvable, semiabelian 998
12T156 [33:2]D(4) 432
24 · 33
1 solvable, semiabelian 933
12T157 [(1/3.33):2]S(4)4 432
24 · 33
1 solvable, even 204
12T158 [25]F18(6) 576
26 · 32
2 solvable, semiabelian, even 628
12T159 [25]F18(6)2 576
26 · 32
2 solvable, semiabelian 435
12T160 1/2[S4(6c)2]2 576
26 · 32
1 solvable, semiabelian 301
12T161 [1/2.S4(6c)2]2 576
26 · 32
1 solvable, semiabelian, even 472
12T162 [24]F36(6) 576
26 · 32
1 solvable, semiabelian, even 384
12T163 [24]F18(6):2 576
26 · 32
1 solvable, semiabelian, even 497
12T164 [1/9.A(4)3]3 576
26 · 32
1 solvable, semiabelian, even 453
12T165 [1/4E(4)3:3:2]3 576
26 · 32
1 solvable, semiabelian 563
12T166 [1/9.A(4)3]33 576
26 · 32
1 solvable, semiabelian, even 320
12T167 [34]D(4)=3wrD(4) 648
23 · 34
3 solvable, semiabelian 501
12T168 [34:2]E(4) 648
23 · 34
1 solvable, semiabelian, even 339
12T169 1/2[34:2]cD(4) 648
23 · 34
1 solvable, semiabelian 421
12T170 [34:2]4 648
23 · 34
1 solvable, semiabelian 422
12T171 [34:2]E(4)2 648
23 · 34
1 solvable, semiabelian, even 288
12T172 1/2[34:22]E(4) 648
23 · 34
1 solvable, semiabelian, even 452
12T173 [34:2]44 648
23 · 34
1 solvable, semiabelian, even 203
12T174 [34:2]E(4)4 648
23 · 34
1 solvable, semiabelian, even 184
12T175 [33]S(4) 648
23 · 34
1 solvable, semiabelian 384
12T176 [33:2]A(4) 648
23 · 34
1 solvable, semiabelian, even 523
12T177 [33]S(4)6 648
23 · 34
1 solvable, semiabelian 456
12T178 1/2[33:2]S(4) 648
23 · 34
1 solvable, semiabelian 432
12T179 L(2,11) 660
22 · 3 · 5 · 11
1 not solvable, primitive, simple, irreducible, even 26
12T180 A(6)[x]2 720
24 · 32 · 5
2 not solvable, even 306
12T181 M10(12)=[A6[1/360]{M10}A6]22 720
24 · 32 · 5
1 not solvable, irreducible, even 15
12T182 PGL(2,9)(12)=[A6[1/360]{M10}A6]2 720
24 · 32 · 5
1 not solvable, irreducible, even 68
12T183 S6(12) 720
24 · 32 · 5
1 not solvable, irreducible, even 309
12T184 [25]S4(6d) 768
28 · 3
2 solvable, semiabelian, even 1029
12T185 [1/4.cD(4)3]S(3) 768
28 · 3
2 solvable, semiabelian 1233
12T186 [1/4.eD(4)3]S(3) 768
28 · 3
2 solvable, semiabelian 1836
12T187 [25]2A4(6) 768
28 · 3
2 solvable, even 1335
12T188 [26]A4=2wrA4(6) 768
28 · 3
2 solvable 1556
12T189 [1/2.cD(4)3]3 768
28 · 3
2 solvable, semiabelian 952
12T190 1/2[26]S4(6d) 768
28 · 3
2 solvable, semiabelian 975
12T191 [25]S4(6c) 768
28 · 3
2 solvable, semiabelian, even 829
12T192 1/2[26]S4(6c) 768
28 · 3
2 solvable, semiabelian 579
12T193 [26]D(6)=2wrD(6) 768
28 · 3
2 solvable, semiabelian 1887
12T194 [34]A(4)=3wrA(4) 972
22 · 35
3 solvable, semiabelian, even 222
12T195 [25]F18(6):2 1152
27 · 32
2 solvable, semiabelian, even 1040
12T196 [25]F18:22 1152
27 · 32
2 solvable, semiabelian 414
12T197 1/2[26]F18:2 1152
27 · 32
2 solvable, semiabelian 731
12T198 1/2[26]F36 1152
27 · 32
2 solvable, semiabelian 693
12T199 [25]F36(6) 1152
27 · 32
2 solvable, semiabelian, even 858
12T200 [S4(6c)2]2=S4(6c)wr2 1152
27 · 32
1 solvable, semiabelian 665
12T201 [24]F36:24 1152
27 · 32
1 solvable, semiabelian 999
12T202 [24]F36:22 1152
27 · 32
1 solvable, semiabelian, even 1182
12T203 [S4(6d)2]2=S4(6d)wr2 1152
27 · 32
1 solvable, semiabelian, even 822
12T204 [1/9.A(4)3]S(3)2 1152
27 · 32
1 solvable, semiabelian 499
12T205 [E(4)3:3:2]3 1152
27 · 32
1 solvable, semiabelian 447
12T206 [1/9.A(4)3]S(3) 1152
27 · 32
1 solvable, semiabelian, even 729
12T207 [1/9.A(4)3]S(3)6 1152
27 · 32
1 solvable, semiabelian 453
12T208 [2A42]2=2A4wr2=2wrF18(6) 1152
27 · 32
2 solvable, semiabelian 1113
12T209 1/2[34:22]cD(4) 1296
24 · 34
1 solvable, semiabelian 637
12T210 [34:22]E(4) 1296
24 · 34
1 solvable, semiabelian, even 707
12T211 [34:22]4 1296
24 · 34
1 solvable, semiabelian 449
12T212 [34:2]D(4)8 1296
24 · 34
1 solvable, semiabelian, even 271
12T213 [33:2]S(4) 1296
24 · 34
1 solvable, semiabelian 676
12T214 [1/2.F362]2 1296
24 · 34
1 solvable, semiabelian, even 344
12T215 1/2[F362]2 1296
24 · 34
1 solvable, semiabelian, even 215
12T216 [34:2]D(4)4 1296
24 · 34
1 solvable, semiabelian, even 411
12T217 [34:2]D(4) 1296
24 · 34
1 solvable, semiabelian 722
12T218 PGL(2,11) 1320
23 · 3 · 5 · 11
1 not solvable, primitive, irreducible 64
12T219 S(6)[x]2 1440
25 · 32 · 5
2 not solvable, even 908
12T220 M10.2(12)=A6.E4(12)=[S6[1/720]{M10}S6]2 1440
25 · 32 · 5
1 not solvable, irreducible, even 141
12T221 [1/2.cD(4)3]S(3) 1536
29 · 3
2 solvable, semiabelian 1095
12T222 [D(4)4]3=D(4)wr3 1536
29 · 3
2 solvable, semiabelian 2418
12T223 1/2e[D(4)3]S(3) 1536
29 · 3
2 solvable, semiabelian 1174
12T224 [26]S4(6c)=2wrS4(6c) 1536
29 · 3
2 solvable, semiabelian 1419
12T225 1/2c[D(4)3]S(3) 1536
29 · 3
2 solvable, semiabelian 995
12T226 [25]2S4(6) 1536
29 · 3
2 solvable, semiabelian, even 1577
12T227 [26]S4(6d)=2wrS4(6d) 1536
29 · 3
2 solvable, semiabelian 1901
12T228 1/3[A(4)3]3 1728
26 · 33
1 solvable, semiabelian, even 187
12T229 [1/3.A(4)3]3 1728
26 · 33
1 solvable, semiabelian, even 301
12T230 [25]L(6) 1920
27 · 3 · 5
2 not solvable, even 654
12T231 [34]S(4)=3wrS(4) 1944
23 · 35
3 solvable, semiabelian 324
12T232 [34:2]A(4)4 1944
23 · 35
1 solvable, even 227
12T233 1/2[34:2]S(4) 1944
23 · 35
1 solvable, semiabelian 357
12T234 [34:2]A(4) 1944
23 · 35
1 solvable, semiabelian, even 315
12T235 [25]F36:22{S32,t} 2304
28 · 32
2 solvable, semiabelian 1749
12T236 [25]F36(6):2 2304
28 · 32
2 solvable, semiabelian, even 1729
12T237 [25]F36:22{S32,i} 2304
28 · 32
2 solvable, semiabelian 1614
12T238 [25]F36:22{32:4} 2304
28 · 32
2 solvable, semiabelian 1632
12T239 [E(4)3:3:2]3 2304
28 · 32
1 solvable, semiabelian 881
12T240 [26]F18:2=2wrF18(6):2 2304
28 · 32
2 solvable, semiabelian 1716
12T241 [26]F36=2wrF36(6) 2304
28 · 32
2 solvable, semiabelian 1560
12T242 [34:23]E(4) 2592
25 · 34
1 solvable, semiabelian, even 329
12T243 [34:22]D(4)4 2592
25 · 34
1 solvable, semiabelian, even 236
12T244 1/2[S(3)4]4 2592
25 · 34
1 solvable, semiabelian, even 364
12T245 [34:23]4 2592
25 · 34
1 solvable, semiabelian 199
12T246 1/2[S(3)4]E(4) 2592
25 · 34
1 solvable, semiabelian 196
12T247 [34:22]D(4)2 2592
25 · 34
1 solvable, semiabelian 335
12T248 [34:22]D(4) 2592
25 · 34
1 solvable, semiabelian 679
12T249 [F362]2=F36wr2 2592
25 · 34
1 solvable, semiabelian, even 189
12T250 [D(4)4]S(3)=D(4)wrS(3) 3072
210 · 3
2 solvable, semiabelian 2825
12T251 [1/3.A(4)3]S(3)2 3456
27 · 33
1 solvable, semiabelian 493
12T252 [1/3.A(4)3]S(3) 3456
27 · 33
1 solvable, semiabelian, even 660
12T253 [E(4)3:32:2]3 3456
27 · 33
1 solvable, semiabelian 537
12T254 [1/3.A(4)3]S(3)6 3456
27 · 33
1 solvable, semiabelian 319
12T255 [26]L(6)=2wrL(6) 3840
28 · 3 · 5
2 not solvable 1289
12T256 1/2[26]L(6):2 3840
28 · 3 · 5
2 not solvable 629
12T257 [25]L(6):2 3840
28 · 3 · 5
2 not solvable, even 634
12T258 [34:2]S(4) 3888
24 · 35
1 solvable, semiabelian 589
12T259 [34:2]S(4)8 3888
24 · 35
1 solvable, even 200
12T260 [2S42]2=2S4wr2 4608
29 · 32
2 solvable, semiabelian 2661
12T261 [S(3)4]E(4)=S(3)wrE(4) 5184
26 · 34
1 solvable, semiabelian 357
12T262 1/2[S(3)4]dD(4) 5184
26 · 34
1 solvable, semiabelian 249
12T263 1/2[S(3)4]cD(4) 5184
26 · 34
1 solvable, semiabelian 416
12T264 [S(3)4]4=S(3)wr4 5184
26 · 34
1 solvable, semiabelian 466
12T265 [A(4)3]3=A(4)wr3 5184
26 · 34
1 solvable, semiabelian, even 290
12T266 1/2[S(3)4]eD(4) 5184
26 · 34
1 solvable, semiabelian, even 462
12T267 [34:23]D(4) 5184
26 · 34
1 solvable, semiabelian 588
12T268 [E(4)3:32:2]S(3) 6912
28 · 33
1 solvable, semiabelian 881
12T269 [L(6)2]2=L(6)wr2 7200
25 · 32 · 52
1 not solvable, irreducible, even 196
12T270 [26]L(6):2=2wrL(6):2 7680
29 · 3 · 5
2 not solvable 1333
12T271 [34:23]A(4) 7776
25 · 35
1 solvable, even 192
12T272 M11(12) 7920
24 · 32 · 5 · 11
1 not solvable, primitive, simple, irreducible, even 35
12T273 [1/4.S(4)3]3 10368
27 · 34
1 solvable, semiabelian 327
12T274 [S(3)4]D(4)=S(3)wrD(4) 10368
27 · 34
1 solvable, semiabelian 876
12T275 [A(4)3]S(3)=A(4)wrS(3) 10368
27 · 34
1 solvable, semiabelian, even 445
12T276 1/2[1/4.S(4)3]S(3) 10368
27 · 34
1 solvable, semiabelian 308
12T277 [25]A(6) 11520
28 · 32 · 5
2 not solvable, even 513
12T278 1/2[(L(6):2)2]2 14400
26 · 32 · 52
1 not solvable, irreducible 116
12T279 [1/2.(L(6):2)2]2 14400
26 · 32 · 52
1 not solvable, irreducible, even 250
12T280 [S(3)4]A(4)=S(3)wrA(4) 15552
26 · 35
1 solvable 358
12T281 [34:23]S(4) 15552
26 · 35
1 solvable, semiabelian 238
12T282 1/2[S(3)4]S(4) 15552
26 · 35
1 solvable, even 100
12T283 [1/4.S(4)3]S(3) 20736
28 · 34
1 solvable, semiabelian 609
12T284 [1/2.S(4)3]3 20736
28 · 34
1 solvable, semiabelian, even 444
12T285 [25]S(6) 23040
29 · 32 · 5
2 not solvable, even 1487
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 777
12T288 [(L(6):2)2]2=L(6):2wr2 28800
27 · 32 · 52
1 not solvable, irreducible 314
12T289 [S(3)4]S(4)=S(3)wrS(4) 31104
27 · 35
1 solvable 659
12T290 [1/2.S(4)3]S(3) 41472
29 · 34
1 solvable, semiabelian, even 619
12T291 1/2[S(4)3]S(3) 41472
29 · 34
1 solvable, semiabelian 512
12T292 [S(4)3]3=S(4)wr3 41472
29 · 34
1 solvable, semiabelian 1033
12T293 [26]S(6)=2wrS(6) 46080
210 · 32 · 5
2 not solvable 2410
12T294 [S(4)3]S(3)=S(4)wrS(3) 82944
210 · 34
1 solvable, semiabelian 1143
12T295 M(12) 95040
26 · 33 · 5 · 11
1 not solvable, primitive, simple, irreducible, even 51
12T296 [A(6)2]2=A(6)wr2 259200
27 · 34 · 52
1 not solvable, irreducible, even 360
12T297 [1/2.S(6)2]2 518400
28 · 34 · 52
1 not solvable, irreducible, even 546
12T298 1/2[S(6)2]2 518400
28 · 34 · 52
1 not solvable, irreducible 185
12T299 [S(6)2]2=S(6)wr2 1036800
29 · 34 · 52
1 not solvable, irreducible 1114
12T300 A(12) 239500800
29 · 35 · 52 · 7 · 11
1 not solvable, primitive, simple, irreducible, even 122
12T301 S(12) 479001600
210 · 35 · 52 · 7 · 11
1 not solvable, primitive, irreducible 294

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