# Gap code for working with transitive group 18T47


# Define the Galois group: 
G := TransitiveGroup(18, 47);

# Abstract group ID: 
IdGroup(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: 
if IsNilpotentGroup(G) then NilpotencyClassOfGroup(G); fi;

# Degree: 
NrMovedPoints(G);

# Transitive number: 
TransitiveIdentification(G);

# Parity: 
ForAll(GeneratorsOfGroup(G), g -> SignPerm(g) = 1);

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

# Order of the centralizer of G in S_n: 
Order(Centralizer(SymmetricGroup(18), G));

# Generators: 
GeneratorsOfGroup(G);

# Conjugacy classes: 
ConjugacyClasses(G);

# Character table: 
CharacterTable(G);