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Transitive Groups of degree 9

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Transitive Groups of degree 9
G Name |G| |G| fact. Δ |Z(G)| Properties of G # fields
9T34 S(9) 362880
27 · 34 · 5 · 7
1 not solvable, primitive, irreducible 1005
9T26 E(9):2S4 432
24 · 33
1 solvable, primitive 182
9T27 L(9)=PSL(2,8) 504
23 · 32 · 7
1 not solvable, primitive, simple, irreducible, even 117
9T28 [S(3)3]3=S(3)wr3 648
23 · 34
1 solvable, semiabelian 726
9T29 [1/2.S(3)3]S(3) 648
23 · 34
1 solvable, semiabelian 317
9T30 1/2[S(3)3]S(3) 648
23 · 34
1 solvable, semiabelian, even 414
9T31 [S(3)3]S(3)=S(3)wrS(3) 1296
24 · 34
1 solvable, semiabelian 898
9T32 L(9):3=P|L(2,8) 1512
23 · 33 · 7
1 not solvable, primitive, irreducible, even 319
9T33 A(9) 181440
26 · 34 · 5 · 7
1 not solvable, primitive, simple, irreducible, even 292
9T3 D(9)=9:2 18
2 · 32
1 solvable, semiabelian, even 100
9T5 S(3)[1/2]S(3)=32:2 18
2 · 32
1 solvable, semiabelian, even 228
9T8 S(3)[x]S(3)=E(9):D4 36
22 · 32
1 solvable, semiabelian 571
9T9 E(9):4 36
22 · 32
1 solvable, primitive, semiabelian, even 115
9T10 [32]S(3)6 54
2 · 33
1 solvable, semiabelian, even 177
9T11 E(9):6=1/2[32:2]S(3) 54
2 · 33
1 solvable, semiabelian, even 156
9T13 E(9):D6=[32:2]3=[1/2.S(3)2]3 54
2 · 33
1 solvable, semiabelian 166
9T14 M(9)=E(9):Q8 72
23 · 32
1 solvable, primitive, semiabelian, even 132
9T15 E(9):8 72
23 · 32
1 solvable, primitive, semiabelian 101
9T16 E(9):D8 72
23 · 32
1 solvable, primitive, semiabelian 225
9T18 E(9):D12=[32:2]S(3)=[1/2.S(3)2]S(3) 108
22 · 33
1 solvable, semiabelian 439
9T19 E(9):2D8 144
24 · 32
1 solvable, primitive, semiabelian 189
9T21 1/2.[33:2]S(3) 162
2 · 34
1 solvable, semiabelian, even 288
9T22 [33:2]3 162
2 · 34
1 solvable, semiabelian 184
9T23 E(9):2A4 216
23 · 33
1 solvable, primitive, even 90
9T24 [33:2]S(3) 324
22 · 34
1 solvable, semiabelian 512
9T25 [1/2.S(3)3]3 324
22 · 34
1 solvable, semiabelian, even 245
9T12 [32]S(3) 54
2 · 33
3 solvable, semiabelian 187
9T17 [33]3=3wr3 81
34
3 nilpotent, semiabelian, even 62
9T4 S(3)[x]3 18
2 · 32
3 solvable, semiabelian 417
9T20 [33]S(3)=3wrS(3) 162
2 · 34
3 solvable, semiabelian 206
9T6 1/3[33]3 27
33
3 nilpotent, semiabelian, even 84
9T7 E(9):3=[32]3 27
33
3 nilpotent, semiabelian, even 88
9T1 C(9)=9 9
32
9 cyclic, semiabelian, even 40
9T2 E(9)=3[x]3 9
32
9 abelian, semiabelian, even 57

9   |   2,85 ms