<< degree 21 | overview | degree 23 >>
| Transitive Groups of degree 22 | ||||||
| G | Name | |G| | |G| fact. | |Z(G)| | Properties of G | # fields |
|---|---|---|---|---|---|---|
| 22T1 | 22 | 22 |
2 · 11
|
22 | cyclic, semiabelian | 133 |
| 22T2 | t22n2 | 22 |
2 · 11
|
1 | solvable, semiabelian | 67 |
| 22T3 | t22n3 | 44 |
22 · 11
|
2 | solvable, semiabelian | 257 |
| 22T4 | t22n4 | 110 |
2 · 5 · 11
|
1 | solvable, semiabelian | 101 |
| 22T5 | t22n5 | 110 |
2 · 5 · 11
|
2 | solvable, semiabelian | 148 |
| 22T6 | t22n6 | 220 |
22 · 5 · 11
|
2 | solvable, semiabelian | 392 |
| 22T7 | t22n7 | 242 |
2 · 112
|
11 | solvable, semiabelian | 84 |
| 22T8 | t22n8 | 484 |
22 · 112
|
1 | solvable, semiabelian, even | 24 |
| 22T9 | t22n9 | 484 |
22 · 112
|
1 | solvable, semiabelian | 163 |
| 22T10 | t22n10 | 968 |
23 · 112
|
1 | solvable, semiabelian | 8 |
| 22T11 | t22n11 | 1210 |
2 · 5 · 112
|
1 | solvable, semiabelian | 72 |
| 22T12 | t22n12 | 1210 |
2 · 5 · 112
|
1 | solvable, semiabelian | 90 |
| 22T13 | t22n13 | 1320 |
23 · 3 · 5 · 11
|
2 | not solvable | 359 |
| 22T14 | t22n14 | 1320 |
23 · 3 · 5 · 11
|
1 | not solvable, irreducible | 139 |
| 22T15 | t22n15 | 2420 |
22 · 5 · 112
|
1 | solvable, semiabelian | 139 |
| 22T16 | t22n16 | 2420 |
22 · 5 · 112
|
1 | solvable, semiabelian, even | 6 |
| 22T17 | t22n17 | 2420 |
22 · 5 · 112
|
1 | solvable, semiabelian | 29 |
| 22T18 | t22n18 | 2420 |
22 · 5 · 112
|
1 | solvable, semiabelian, even | 86 |
| 22T19 | t22n19 | 4840 |
23 · 5 · 112
|
1 | solvable, semiabelian | 7 |
| 22T20 | t22n20 | 4840 |
23 · 5 · 112
|
1 | solvable, semiabelian | 260 |
| 22T21 | t22n21 | 6050 |
2 · 52 · 112
|
1 | solvable, semiabelian | 107 |
| 22T22 | t22n22 | 7920 |
24 · 32 · 5 · 11
|
1 | not solvable, simple, irreducible, even | 42 |
| 22T23 | t22n23 | 11264 |
210 · 11
|
1 | solvable, semiabelian, even | 2669 |
| 22T24 | t22n24 | 12100 |
22 · 52 · 112
|
1 | solvable, semiabelian, even | 40 |
| 22T25 | t22n25 | 12100 |
22 · 52 · 112
|
1 | solvable, semiabelian | 28 |
| 22T26 | t22n26 | 15840 |
25 · 32 · 5 · 11
|
2 | not solvable | 209 |
| 22T27 | t22n27 | 15840 |
25 · 32 · 5 · 11
|
2 | not solvable | 277 |
| 22T28 | t22n28 | 22528 |
211 · 11
|
2 | solvable, semiabelian | 4812 |
| 22T29 | t22n29 | 22528 |
211 · 11
|
1 | solvable, semiabelian | 2611 |
| 22T30 | t22n30 | 22528 |
211 · 11
|
1 | solvable, semiabelian, even | 2480 |
| 22T31 | t22n31 | 24200 |
23 · 52 · 112
|
1 | solvable, semiabelian | 44 |
| 22T32 | t22n32 | 45056 |
212 · 11
|
2 | solvable, semiabelian | 4661 |
| 22T33 | t22n33 | 56320 |
210 · 5 · 11
|
1 | solvable, semiabelian, even | 2246 |
| 22T34 | t22n34 | 112640 |
211 · 5 · 11
|
1 | solvable, semiabelian, even | 1175 |
| 22T35 | t22n35 | 112640 |
211 · 5 · 11
|
1 | solvable, semiabelian | 1190 |
| 22T36 | t22n36 | 112640 |
211 · 5 · 11
|
2 | solvable, semiabelian | 5644 |
| 22T37 | t22n37 | 225280 |
212 · 5 · 11
|
2 | solvable, semiabelian | 4232 |
| 22T38 | M(22) | 443520 |
27 · 32 · 5 · 7 · 11
|
1 | not solvable, primitive, simple, irreducible, even | 15 |
| 22T39 | t22n39 | 675840 |
212 · 3 · 5 · 11
|
1 | not solvable, even | 1415 |
| 22T40 | t22n40 | 871200 |
25 · 32 · 52 · 112
|
1 | not solvable, irreducible | 6 |
| 22T41 | M(22):2 | 887040 |
28 · 32 · 5 · 7 · 11
|
1 | not solvable, primitive, irreducible | 253 |
| 22T42 | t22n42 | 1351680 |
213 · 3 · 5 · 11
|
2 | not solvable | 3450 |
| 22T43 | t22n43 | 8110080 |
214 · 32 · 5 · 11
|
1 | not solvable, even | 660 |
| 22T44 | t22n44 | 16220160 |
215 · 32 · 5 · 11
|
2 | not solvable | 1482 |
| 22T45 | t22n45 | 39916800 |
28 · 34 · 52 · 7 · 11
|
1 | not solvable, irreducible | 242 |
| 22T46 | t22n46 | 39916800 |
28 · 34 · 52 · 7 · 11
|
2 | not solvable | 464 |
| 22T47 | t22n47 | 79833600 |
29 · 34 · 52 · 7 · 11
|
2 | not solvable | 1225 |
| 22T48 | t22n48 | 125452800 |
29 · 34 · 52 · 112
|
1 | not solvable, irreducible | 8 |
| 22T49 | t22n49 | 20437401600 |
217 · 34 · 52 · 7 · 11
|
1 | not solvable, even | 775 |
| 22T50 | t22n50 | 40874803200 |
218 · 34 · 52 · 7 · 11
|
1 | not solvable | 928 |
| 22T51 | t22n51 | 40874803200 |
218 · 34 · 52 · 7 · 11
|
1 | not solvable, even | 957 |
| 22T52 | t22n52 | 40874803200 |
218 · 34 · 52 · 7 · 11
|
2 | not solvable | 2047 |
| 22T53 | t22n53 | 81749606400 |
219 · 34 · 52 · 7 · 11
|
2 | not solvable | 1947 |
| 22T54 | t22n54 | 796675461120000 |
215 · 38 · 54 · 72 · 112
|
1 | not solvable, irreducible | 6 |
| 22T55 | t22n55 | 1593350922240000 |
216 · 38 · 54 · 72 · 112
|
1 | not solvable, irreducible, even | 10 |
| 22T56 | t22n56 | 1593350922240000 |
216 · 38 · 54 · 72 · 112
|
1 | not solvable, irreducible | 15 |
| 22T57 | t22n57 | 3186701844480000 |
217 · 38 · 54 · 72 · 112
|
1 | not solvable, irreducible | 2179 |
| 22T58 | Alt(22) | 562000363888803840000 |
218 · 39 · 54 · 73 · 112 · 13 · 17 · 19
|
1 | not solvable, primitive, simple, irreducible, even | 2 |
| 22T59 | Sym(22) | 1124000727777607680000 |
219 · 39 · 54 · 73 · 112 · 13 · 17 · 19
|
1 | not solvable, primitive, irreducible | 82 |
9 | 2,53 ms