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Transitive Groups of degree 4

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Transitive Groups of degree 4
Δ G Name |G| |G| fact. |Z(G)| Properties of G # fields
4T1 C(4) = 4 4
22
4 cyclic, semiabelian 436
4T2 E(4) = 2[x]2 4
22
4 abelian, semiabelian, even 362
4T3 D(4) 8
23
2 nilpotent, semiabelian 660
4T4 A(4) 12
22 · 3
1 solvable, primitive, semiabelian, even 374
4T5 S(4) 24
23 · 3
1 solvable, primitive, semiabelian 504

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