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Transitive Groups of degree 17

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Transitive Groups of degree 17
G Name Δ |G| |G| fact. |Z(G)| Properties of G # fields
17T1 C(17)=17 17
17
17 cyclic, primitive, simple, semiabelian, even 4
17T2 D(17)=17:2 34
2 · 17
1 solvable, primitive, semiabelian, even 12
17T3 F68(17)=17:4 68
22 · 17
1 solvable, primitive, semiabelian, even 4
17T4 F136(17)=17:8 136
23 · 17
1 solvable, primitive, semiabelian, even 2
17T5 F272(17)=17:16 272
24 · 17
1 solvable, primitive, semiabelian 68
17T6 L(17)=PSL(2,16) 4080
24 · 3 · 5 · 17
1 not solvable, primitive, simple, irreducible, even 3
17T7 L(17):2=<PZL(2,16) 8160
25 · 3 · 5 · 17
1 not solvable, primitive, irreducible, even 0
17T8 L(17):4=PYL(2,16) 16320
26 · 3 · 5 · 17
1 not solvable, primitive, irreducible, even 4
17T9 A17 177843714048000
214 · 36 · 53 · 72 · 11 · 13 · 17
1 not solvable, primitive, simple, irreducible, even 9
17T10 S17 355687428096000
215 · 36 · 53 · 72 · 11 · 13 · 17
1 not solvable, primitive, irreducible 52

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