<< degree 20 | overview | degree 22 >>
| 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 | 92 |
| 21T2 | t21n2 | 21 |
3 · 7
|
1 | solvable, semiabelian, even | 51 |
| 21T3 | t21n3 | 42 |
2 · 3 · 7
|
3 | solvable, semiabelian | 171 |
| 21T4 | t21n4 | 42 |
2 · 3 · 7
|
1 | solvable, semiabelian | 169 |
| 21T5 | t21n5 | 42 |
2 · 3 · 7
|
1 | solvable, semiabelian, even | 83 |
| 21T6 | t21n6 | 42 |
2 · 3 · 7
|
7 | solvable, semiabelian | 245 |
| 21T7 | t21n7 | 63 |
32 · 7
|
3 | solvable, semiabelian, even | 145 |
| 21T8 | t21n8 | 84 |
22 · 3 · 7
|
1 | solvable, semiabelian | 370 |
| 21T9 | t21n9 | 126 |
2 · 32 · 7
|
3 | solvable, semiabelian | 268 |
| 21T10 | t21n10 | 126 |
2 · 32 · 7
|
1 | solvable, semiabelian, even | 195 |
| 21T11 | t21n11 | 126 |
2 · 32 · 7
|
1 | solvable, semiabelian | 320 |
| 21T12 | t21n12 | 147 |
3 · 72
|
1 | solvable, semiabelian, even | 48 |
| 21T13 | t21n13 | 147 |
3 · 72
|
7 | solvable, semiabelian, even | 71 |
| 21T14 | t21n14 | 168 |
23 · 3 · 7
|
1 | not solvable, simple, irreducible, even | 255 |
| 21T15 | t21n15 | 252 |
22 · 32 · 7
|
1 | solvable, semiabelian | 556 |
| 21T16 | t21n16 | 294 |
2 · 3 · 72
|
1 | solvable, semiabelian | 99 |
| 21T17 | t21n17 | 294 |
2 · 3 · 72
|
1 | solvable, semiabelian, even | 119 |
| 21T18 | t21n18 | 294 |
2 · 3 · 72
|
1 | solvable, semiabelian | 106 |
| 21T19 | t21n19 | 294 |
2 · 3 · 72
|
1 | solvable, semiabelian | 66 |
| 21T20 | PGL(2, 7) | 336 |
24 · 3 · 7
|
1 | not solvable, primitive, irreducible | 265 |
| 21T21 | t21n21 | 441 |
32 · 72
|
1 | solvable, semiabelian, even | 42 |
| 21T22 | t21n22 | 504 |
23 · 32 · 7
|
3 | not solvable, even | 298 |
| 21T23 | t21n23 | 588 |
22 · 3 · 72
|
1 | solvable, semiabelian | 160 |
| 21T24 | t21n24 | 882 |
2 · 32 · 72
|
1 | solvable, semiabelian | 81 |
| 21T25 | t21n25 | 882 |
2 · 32 · 72
|
1 | solvable, semiabelian, even | 90 |
| 21T26 | t21n26 | 882 |
2 · 32 · 72
|
1 | solvable, semiabelian | 95 |
| 21T27 | t21n27 | 1008 |
24 · 32 · 7
|
1 | not solvable | 582 |
| 21T28 | t21n28 | 1029 |
3 · 73
|
7 | solvable, semiabelian, even | 176 |
| 21T29 | t21n29 | 1764 |
22 · 32 · 72
|
1 | solvable, semiabelian | 272 |
| 21T30 | t21n30 | 2058 |
2 · 3 · 73
|
1 | solvable, semiabelian, even | 277 |
| 21T31 | t21n31 | 2058 |
2 · 3 · 73
|
1 | solvable, semiabelian | 181 |
| 21T32 | t21n32 | 2058 |
2 · 3 · 73
|
7 | solvable, semiabelian | 299 |
| 21T33 | A(7) | 2520 |
23 · 32 · 5 · 7
|
1 | not solvable, primitive, simple, irreducible, even | 372 |
| 21T34 | t21n34 | 3087 |
32 · 73
|
1 | solvable, semiabelian, even | 113 |
| 21T35 | t21n35 | 3087 |
32 · 73
|
1 | solvable, semiabelian, even | 173 |
| 21T36 | t21n36 | 4116 |
22 · 3 · 73
|
1 | solvable, semiabelian, even | 174 |
| 21T37 | t21n37 | 4116 |
22 · 3 · 73
|
1 | solvable, semiabelian | 564 |
| 21T38 | S(7) | 5040 |
24 · 32 · 5 · 7
|
1 | not solvable, primitive, irreducible | 522 |
| 21T39 | t21n39 | 5103 |
36 · 7
|
1 | solvable, semiabelian, even | 127 |
| 21T40 | t21n40 | 6174 |
2 · 32 · 73
|
1 | solvable, semiabelian | 356 |
| 21T41 | t21n41 | 6174 |
2 · 32 · 73
|
1 | solvable, semiabelian, even | 86 |
| 21T42 | t21n42 | 6174 |
2 · 32 · 73
|
1 | solvable, semiabelian | 133 |
| 21T43 | t21n43 | 6174 |
2 · 32 · 73
|
1 | solvable, semiabelian | 122 |
| 21T44 | t21n44 | 7560 |
23 · 33 · 5 · 7
|
3 | not solvable, even | 252 |
| 21T45 | t21n45 | 8232 |
23 · 3 · 73
|
1 | solvable, semiabelian | 290 |
| 21T46 | t21n46 | 8232 |
23 · 3 · 73
|
1 | solvable, semiabelian | 266 |
| 21T47 | t21n47 | 8232 |
23 · 3 · 73
|
1 | solvable, semiabelian, even | 211 |
| 21T48 | t21n48 | 9261 |
33 · 73
|
1 | solvable, semiabelian, even | 124 |
| 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 | 248 |
| 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 | 438 |
| 21T56 | t21n56 | 15120 |
24 · 33 · 5 · 7
|
3 | not solvable | 498 |
| 21T57 | t21n57 | 15120 |
24 · 33 · 5 · 7
|
1 | not solvable | 551 |
| 21T58 | t21n58 | 15120 |
24 · 33 · 5 · 7
|
1 | not solvable, even | 277 |
| 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 | 635 |
| 21T63 | t21n63 | 18522 |
2 · 33 · 73
|
1 | solvable, semiabelian | 78 |
| 21T64 | t21n64 | 18522 |
2 · 33 · 73
|
1 | solvable, semiabelian, even | 70 |
| 21T65 | t21n65 | 18522 |
2 · 33 · 73
|
1 | solvable, semiabelian | 217 |
| 21T66 | t21n66 | 18522 |
2 · 33 · 73
|
1 | solvable, semiabelian | 62 |
| 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 | 98 |
| 21T71 | t21n71 | 24696 |
23 · 32 · 73
|
1 | solvable, semiabelian | 28 |
| 21T72 | t21n72 | 24696 |
23 · 32 · 73
|
1 | solvable, semiabelian, even | 41 |
| 21T73 | t21n73 | 27783 |
34 · 73
|
1 | solvable, semiabelian, even | 114 |
| 21T74 | t21n74 | 30240 |
25 · 33 · 5 · 7
|
1 | not solvable | 993 |
| 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 | 239 |
| 21T78 | t21n78 | 30618 |
2 · 37 · 7
|
1 | solvable, semiabelian, even | 140 |
| 21T79 | t21n79 | 30618 |
2 · 37 · 7
|
1 | solvable, semiabelian | 249 |
| 21T80 | t21n80 | 30618 |
2 · 37 · 7
|
1 | solvable, semiabelian | 300 |
| 21T81 | t21n81 | 30618 |
2 · 37 · 7
|
1 | solvable, semiabelian | 141 |
| 21T82 | t21n82 | 37044 |
22 · 33 · 73
|
1 | solvable, semiabelian | 196 |
| 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 | 403 |
| 21T88 | t21n88 | 55566 |
2 · 34 · 73
|
1 | solvable, semiabelian, even | 30 |
| 21T89 | t21n89 | 55566 |
2 · 34 · 73
|
1 | solvable, semiabelian | 80 |
| 21T90 | t21n90 | 55566 |
2 · 34 · 73
|
1 | solvable, semiabelian | 353 |
| 21T91 | PGL(3, 4) | 60480 |
26 · 33 · 5 · 7
|
1 | not solvable, primitive, irreducible, even | 45 |
| 21T92 | t21n92 | 61236 |
22 · 37 · 7
|
1 | solvable, semiabelian | 323 |
| 21T93 | t21n93 | 61236 |
22 · 37 · 7
|
1 | solvable, semiabelian | 829 |
| 21T94 | t21n94 | 74088 |
23 · 33 · 73
|
1 | solvable, semiabelian | 119 |
| 21T95 | t21n95 | 74088 |
23 · 33 · 73
|
1 | solvable, semiabelian, even | 25 |
| 21T96 | t21n96 | 74088 |
23 · 33 · 73
|
1 | solvable, semiabelian | 86 |
| 21T97 | t21n97 | 74088 |
23 · 33 · 73
|
1 | solvable, semiabelian | 26 |
| 21T98 | t21n98 | 91854 |
2 · 38 · 7
|
3 | solvable, semiabelian | 218 |
| 21T99 | t21n99 | 91854 |
2 · 38 · 7
|
1 | solvable, semiabelian, even | 182 |
| 21T100 | t21n100 | 91854 |
2 · 38 · 7
|
1 | solvable, semiabelian | 418 |
| 21T101 | t21n101 | 111132 |
22 · 34 · 73
|
1 | solvable, semiabelian, even | 31 |
| 21T102 | t21n102 | 111132 |
22 · 34 · 73
|
1 | solvable, semiabelian | 189 |
| 21T103 | PGammaL(3, 4) | 120960 |
27 · 33 · 5 · 7
|
1 | not solvable, primitive, irreducible | 149 |
| 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 | 340 |
| 21T107 | t21n107 | 183708 |
22 · 38 · 7
|
1 | solvable, semiabelian | 404 |
| 21T108 | t21n108 | 222264 |
23 · 34 · 73
|
1 | solvable, semiabelian, even | 84 |
| 21T109 | t21n109 | 222264 |
23 · 34 · 73
|
1 | solvable, semiabelian | 531 |
| 21T110 | t21n110 | 222264 |
23 · 34 · 73
|
1 | solvable, semiabelian | 29 |
| 21T111 | t21n111 | 244944 |
24 · 37 · 7
|
1 | not solvable | 342 |
| 21T112 | t21n112 | 244944 |
24 · 37 · 7
|
1 | solvable, semiabelian | 255 |
| 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 | 848 |
| 21T117 | t21n117 | 734832 |
24 · 38 · 7
|
1 | solvable, semiabelian | 278 |
| 21T118 | t21n118 | 734832 |
24 · 38 · 7
|
1 | not solvable | 444 |
| 21T119 | t21n119 | 734832 |
24 · 38 · 7
|
1 | not solvable | 170 |
| 21T120 | t21n120 | 979776 |
26 · 37 · 7
|
1 | solvable, semiabelian, even | 363 |
| 21T121 | t21n121 | 1837080 |
23 · 38 · 5 · 7
|
1 | not solvable, even | 65 |
| 21T122 | t21n122 | 1959552 |
27 · 37 · 7
|
1 | solvable, semiabelian | 425 |
| 21T123 | t21n123 | 1959552 |
27 · 37 · 7
|
1 | solvable, semiabelian | 719 |
| 21T124 | t21n124 | 1959552 |
27 · 37 · 7
|
1 | solvable, semiabelian, even | 421 |
| 21T125 | t21n125 | 2939328 |
26 · 38 · 7
|
1 | not solvable, even | 329 |
| 21T126 | t21n126 | 2939328 |
26 · 38 · 7
|
1 | not solvable, even | 71 |
| 21T127 | t21n127 | 2939328 |
26 · 38 · 7
|
1 | solvable, semiabelian, even | 334 |
| 21T128 | t21n128 | 3674160 |
24 · 38 · 5 · 7
|
1 | not solvable | 309 |
| 21T129 | t21n129 | 3674160 |
24 · 38 · 5 · 7
|
1 | not solvable, even | 253 |
| 21T130 | t21n130 | 3674160 |
24 · 38 · 5 · 7
|
1 | not solvable | 292 |
| 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 | 434 |
| 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 | 620 |
| 21T137 | t21n137 | 5878656 |
27 · 38 · 7
|
1 | solvable, semiabelian | 120 |
| 21T138 | t21n138 | 7348320 |
25 · 38 · 5 · 7
|
1 | not solvable | 629 |
| 21T139 | t21n139 | 11022480 |
24 · 39 · 5 · 7
|
3 | not solvable | 400 |
| 21T140 | t21n140 | 11022480 |
24 · 39 · 5 · 7
|
1 | not solvable | 426 |
| 21T141 | t21n141 | 11022480 |
24 · 39 · 5 · 7
|
1 | not solvable, even | 330 |
| 21T142 | t21n142 | 11757312 |
28 · 38 · 7
|
1 | solvable, semiabelian | 200 |
| 21T143 | t21n143 | 14224896 |
29 · 34 · 73
|
1 | not solvable, irreducible, even | 409 |
| 21T144 | t21n144 | 22044960 |
25 · 39 · 5 · 7
|
1 | not solvable | 806 |
| 21T145 | t21n145 | 23514624 |
29 · 38 · 7
|
1 | not solvable, even | 582 |
| 21T146 | t21n146 | 28449792 |
210 · 34 · 73
|
1 | not solvable, irreducible | 771 |
| 21T147 | t21n147 | 47029248 |
210 · 38 · 7
|
1 | not solvable | 216 |
| 21T148 | t21n148 | 352719360 |
29 · 39 · 5 · 7
|
1 | not solvable, even | 440 |
| 21T149 | t21n149 | 705438720 |
210 · 39 · 5 · 7
|
1 | not solvable | 748 |
| 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 | 543 |
| 21T154 | t21n154 | 96018048000 |
210 · 37 · 53 · 73
|
1 | not solvable, irreducible | 146 |
| 21T155 | t21n155 | 96018048000 |
210 · 37 · 53 · 73
|
1 | not solvable, irreducible, even | 79 |
| 21T156 | t21n156 | 96018048000 |
210 · 37 · 53 · 73
|
1 | not solvable, irreducible | 985 |
| 21T157 | t21n157 | 192036096000 |
211 · 37 · 53 · 73
|
1 | not solvable, irreducible | 384 |
| 21T158 | t21n158 | 192036096000 |
211 · 37 · 53 · 73
|
1 | not solvable, irreducible, even | 105 |
| 21T159 | t21n159 | 384072192000 |
212 · 37 · 53 · 73
|
1 | not solvable, irreducible | 1667 |
| 21T160 | t21n160 | 384072192000 |
212 · 37 · 53 · 73
|
1 | not solvable, irreducible | 220 |
| 21T161 | t21n161 | 384072192000 |
212 · 37 · 53 · 73
|
1 | not solvable, irreducible, even | 141 |
| 21T162 | t21n162 | 768144384000 |
213 · 37 · 53 · 73
|
1 | not solvable, irreducible | 2269 |
| 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 |
9 | 4,53 ms