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Transitive Groups of degree 19

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Transitive Groups of degree 19
G Name |G| |G| fact. |Z(G)| Properties of G # fields
19T1 C(19)=19 19
19
19 cyclic, primitive, simple, semiabelian, even 3
19T2 D(19)=19:2 38
2 · 19
1 solvable, primitive, semiabelian 12
19T3 F57(19)=19:3 57
3 · 19
1 solvable, primitive, semiabelian, even 2
19T4 F114(19)=19:6 114
2 · 3 · 19
1 solvable, primitive, semiabelian 3
19T5 F171(19)=19:9 171
32 · 19
1 solvable, primitive, semiabelian, even 1
19T6 F342(19)=19:18 342
2 · 32 · 19
1 solvable, primitive, semiabelian 31
19T7 A19 60822550204416000
215 · 38 · 53 · 72 · 11 · 13 · 17 · 19
1 not solvable, primitive, simple, irreducible, even 8
19T8 S19 121645100408832000
216 · 38 · 53 · 72 · 11 · 13 · 17 · 19
1 not solvable, primitive, irreducible 39

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