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Transitive Groups of degree 6

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Transitive Groups of degree 6
G Name |G| |G| fact. Δ |Z(G)| Properties of G # fields
6T16 S(6) 720
24 · 32 · 5
1 not solvable, primitive, irreducible 724
6T2 D6(6) = [3]2 6
2 · 3
1 solvable, semiabelian 220
6T10 F36(6) = 1/2[S(3)2]2 36
22 · 32
1 solvable, semiabelian, even 218
6T12 L(6) = PSL(2,5) = A5(6) 60
22 · 3 · 5
1 not solvable, primitive, simple, irreducible, even 353
6T13 F36(6):2 = [S(3)2]2 = S(3) wr 2 72
23 · 32
1 solvable, semiabelian 828
6T14 L(6):2 = PGL(2,5) = S5(6) 120
23 · 3 · 5
1 not solvable, primitive, irreducible 377
6T15 A(6) 360
23 · 32 · 5
1 not solvable, primitive, simple, irreducible, even 273
6T4 A4(6) = [22]3 12
22 · 3
1 solvable, semiabelian, even 256
6T7 S4(6d) = [22]S(3) 24
23 · 3
1 solvable, semiabelian, even 332
6T8 S4(6c) = 1/2[23]S(3) 24
23 · 3
1 solvable, semiabelian 371
6T9 F18(6):2 = [1/2.S(3)2]2 36
22 · 32
1 solvable, semiabelian 330
6T3 D(6) = S(3)[x]2 12
22 · 3
2 solvable, semiabelian 465
6T6 2A4(6) = [23]3 = 2 wr 3 24
23 · 3
2 solvable, semiabelian 463
6T11 2S4(6) = [23]S(3) = 2 wr S(3) 48
24 · 3
2 solvable, semiabelian 763
6T5 F18(6) = [32]2 = 3 wr 2 18
2 · 32
3 solvable, semiabelian 253
6T1 C(6) = 6 = 3[x]2 6
2 · 3
6 cyclic, semiabelian 399

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