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Transitive Groups of degree 5

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Transitive Groups of degree 5
G Δ Name |G| |G| fact. |Z(G)| Properties of G # fields
5T4 A(5) 60
22 · 3 · 5
1 not solvable, primitive, simple, irreducible, even 375
5T1 C(5) = 5 5
5
5 cyclic, primitive, simple, semiabelian, even 159
5T2 D(5) = 5:2 10
2 · 5
1 solvable, primitive, semiabelian, even 362
5T3 F(5) = 5:4 20
22 · 5
1 solvable, primitive, semiabelian 281
5T5 S(5) 120
23 · 3 · 5
1 not solvable, primitive, irreducible 591

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