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Transitive Groups of degree 22

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Transitive Groups of degree 22
∇ G Name |G| |G| fact. |Z(G)| Properties of G # fields
22T59 Sym(22) 1124000727777607680000
219 · 39 · 54 · 73 · 112 · 13 · 17 · 19
1 not solvable, primitive, irreducible 82
22T58 Alt(22) 562000363888803840000
218 · 39 · 54 · 73 · 112 · 13 · 17 · 19
1 not solvable, primitive, simple, irreducible, even 2
22T57 t22n57 3186701844480000
217 · 38 · 54 · 72 · 112
1 not solvable, irreducible 2179
22T56 t22n56 1593350922240000
216 · 38 · 54 · 72 · 112
1 not solvable, irreducible 15
22T55 t22n55 1593350922240000
216 · 38 · 54 · 72 · 112
1 not solvable, irreducible, even 10
22T54 t22n54 796675461120000
215 · 38 · 54 · 72 · 112
1 not solvable, irreducible 6
22T53 t22n53 81749606400
219 · 34 · 52 · 7 · 11
2 not solvable 1917
22T52 t22n52 40874803200
218 · 34 · 52 · 7 · 11
2 not solvable 2047
22T51 t22n51 40874803200
218 · 34 · 52 · 7 · 11
1 not solvable, even 925
22T50 t22n50 40874803200
218 · 34 · 52 · 7 · 11
1 not solvable 926
22T49 t22n49 20437401600
217 · 34 · 52 · 7 · 11
1 not solvable, even 775
22T48 t22n48 125452800
29 · 34 · 52 · 112
1 not solvable, irreducible 8
22T47 t22n47 79833600
29 · 34 · 52 · 7 · 11
2 not solvable 1224
22T46 t22n46 39916800
28 · 34 · 52 · 7 · 11
2 not solvable 464
22T45 t22n45 39916800
28 · 34 · 52 · 7 · 11
1 not solvable, irreducible 242
22T44 t22n44 16220160
215 · 32 · 5 · 11
2 not solvable 1482
22T43 t22n43 8110080
214 · 32 · 5 · 11
1 not solvable, even 660
22T42 t22n42 1351680
213 · 3 · 5 · 11
2 not solvable 3450
22T41 M(22):2 887040
28 · 32 · 5 · 7 · 11
1 not solvable, primitive, irreducible 242
22T40 t22n40 871200
25 · 32 · 52 · 112
1 not solvable, irreducible 6
22T39 t22n39 675840
212 · 3 · 5 · 11
1 not solvable, even 1415
22T38 M(22) 443520
27 · 32 · 5 · 7 · 11
1 not solvable, primitive, simple, irreducible, even 15
22T37 t22n37 225280
212 · 5 · 11
2 solvable, semiabelian 4232
22T36 t22n36 112640
211 · 5 · 11
2 solvable, semiabelian 5643
22T35 t22n35 112640
211 · 5 · 11
1 solvable, semiabelian 1190
22T34 t22n34 112640
211 · 5 · 11
1 solvable, semiabelian, even 1175
22T33 t22n33 56320
210 · 5 · 11
1 solvable, semiabelian, even 2246
22T32 t22n32 45056
212 · 11
2 solvable, semiabelian 4657
22T31 t22n31 24200
23 · 52 · 112
1 solvable, semiabelian 44
22T30 t22n30 22528
211 · 11
1 solvable, semiabelian, even 2479
22T29 t22n29 22528
211 · 11
1 solvable, semiabelian 2611
22T28 t22n28 22528
211 · 11
2 solvable, semiabelian 4812
22T27 t22n27 15840
25 · 32 · 5 · 11
2 not solvable 277
22T26 t22n26 15840
25 · 32 · 5 · 11
2 not solvable 209
22T25 t22n25 12100
22 · 52 · 112
1 solvable, semiabelian 28
22T24 t22n24 12100
22 · 52 · 112
1 solvable, semiabelian, even 40
22T23 t22n23 11264
210 · 11
1 solvable, semiabelian, even 2654
22T22 t22n22 7920
24 · 32 · 5 · 11
1 not solvable, simple, irreducible, even 42
22T21 t22n21 6050
2 · 52 · 112
1 solvable, semiabelian 107
22T20 t22n20 4840
23 · 5 · 112
1 solvable, semiabelian 260
22T19 t22n19 4840
23 · 5 · 112
1 solvable, semiabelian 7
22T18 t22n18 2420
22 · 5 · 112
1 solvable, semiabelian, even 86
22T17 t22n17 2420
22 · 5 · 112
1 solvable, semiabelian 29
22T16 t22n16 2420
22 · 5 · 112
1 solvable, semiabelian, even 6
22T15 t22n15 2420
22 · 5 · 112
1 solvable, semiabelian 139
22T14 t22n14 1320
23 · 3 · 5 · 11
1 not solvable, irreducible 139
22T13 t22n13 1320
23 · 3 · 5 · 11
2 not solvable 359
22T12 t22n12 1210
2 · 5 · 112
1 solvable, semiabelian 90
22T11 t22n11 1210
2 · 5 · 112
1 solvable, semiabelian 72
22T10 t22n10 968
23 · 112
1 solvable, semiabelian 8
22T9 t22n9 484
22 · 112
1 solvable, semiabelian 163
22T8 t22n8 484
22 · 112
1 solvable, semiabelian, even 24
22T7 t22n7 242
2 · 112
11 solvable, semiabelian 84
22T6 t22n6 220
22 · 5 · 11
2 solvable, semiabelian 392
22T5 t22n5 110
2 · 5 · 11
2 solvable, semiabelian 148
22T4 t22n4 110
2 · 5 · 11
1 solvable, semiabelian 101
22T3 t22n3 44
22 · 11
2 solvable, semiabelian 257
22T2 t22n2 22
2 · 11
1 solvable, semiabelian 67
22T1 22 22
2 · 11
22 cyclic, semiabelian 132

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