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Transitive Groups of degree 23

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Transitive Groups of degree 23
G Δ Name |G| |G| fact. |Z(G)| Properties of G # fields
23T6 A(23) 12926008369442488320000
218 · 39 · 54 · 73 · 112 · 13 · 17 · 19 · 23
1 not solvable, primitive, simple, irreducible, even 11
23T4 AGL(1,23) 506
2 · 11 · 23
1 solvable, primitive, semiabelian 199
23T1 C(23) 23
23
23 cyclic, primitive, simple, semiabelian, even 41
23T2 D(23)=23:2 46
2 · 23
1 solvable, primitive, semiabelian 10
23T3 F(23)=23:11 253
11 · 23
1 solvable, primitive, semiabelian, even 99
23T5 M(23) 10200960
27 · 32 · 5 · 7 · 11 · 23
1 not solvable, primitive, simple, irreducible, even 0
23T7 S(23) 25852016738884976640000
219 · 39 · 54 · 73 · 112 · 13 · 17 · 19 · 23
1 not solvable, primitive, irreducible 79

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