# SageMath code for working with transitive group 38T23


# Define the Galois group: 
G = TransitiveGroup(38, 23)

# Abstract group ID: 
G.id()

# Order: 
G.order()

# Determine if group is cyclic: 
G.is_cyclic()

# Determine if group is abelian: 
G.is_abelian()

# Determine if group is solvable: 
G.is_solvable()

# Nilpotency class: 
libgap(G).NilpotencyClassOfGroup() if G.is_nilpotent() else -1

# Degree: 
G.degree()

# Transitive number: 
G.transitive_number()

# Parity: 
all(g.SignPerm() == 1 for g in libgap(G).GeneratorsOfGroup())

# Determine if group is primitive: 
G.is_primitive()

# Order of the centralizer of G in S_n: 
SymmetricGroup(38).centralizer(G).order()

# Generators: 
G.gens()

# Conjugacy classes: 
G.conjugacy_classes()

# Character table: 
G.character_table()