// Magma code for working with transitive group 6T5


// Define the Galois group: 
G := TransitiveGroup(6, 5);

// Abstract group ID: 
IdentifyGroup(G);

// Order: 
Order(G);

// Determine if group is cyclic: 
IsCyclic(G);

// Determine if group is abelian: 
IsAbelian(G);

// Determine if group is solvable: 
IsSolvable(G);

// Nilpotency class: 
NilpotencyClass(G);

// Degree: 
t, n := TransitiveGroupIdentification(G); n;

// Transitive number: 
t, n := TransitiveGroupIdentification(G); t;

// Parity: 
IsEven(G);

// Determine if group is primitive: 
IsPrimitive(G);

// Order of the centralizer of G in S_n: 
Order(Centralizer(SymmetricGroup(n), G));

// Generators: 
Generators(G);

// Conjugacy classes: 
ConjugacyClasses(G);

// Character table: 
CharacterTable(G);