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Transitive Groups of degree 5  
G  Name  G  G fact.  Z(G)  Properties of G  # fields 

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 
2^{2} · 5

1  solvable, primitive, semiabelian  282 
5T4  A(5)  60 
2^{2} · 3 · 5

1  not solvable, primitive, simple, irreducible, even  376 
5T5  S(5)  120 
2^{3} · 3 · 5

1  not solvable, primitive, irreducible  591 
9  3,33 ms