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Transitive Groups of degree 7

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Transitive Groups of degree 7
G Name |G| |G| fact. |Z(G)| Properties of G # fields
7T1 C(7) = 7 7
7
7 cyclic, primitive, simple, semiabelian, even 40
7T2 D(7) = 7:2 14
2 · 7
1 solvable, primitive, semiabelian 65
7T3 F21(7) = 7:3 21
3 · 7
1 solvable, primitive, semiabelian, even 48
7T4 F42(7) = 7:6 42
2 · 3 · 7
1 solvable, primitive, semiabelian 98
7T5 L(7) = L(3,2) 168
23 · 3 · 7
1 not solvable, primitive, simple, irreducible, even 375
7T6 A(7) 2520
23 · 32 · 5 · 7
1 not solvable, primitive, simple, irreducible, even 383
7T7 S(7) 5040
24 · 32 · 5 · 7
1 not solvable, primitive, irreducible 504

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