# Oscar code for working with transitive group 32T600
# If you have not already loaded the Oscar package, you should type "using Oscar;" before running the code below.


# Define the Galois group: 
G = transitive_group(32, 600)

# Order: 
order(G)

# Determine if group is cyclic: 
is_cyclic(G)

# Determine if group is abelian: 
is_abelian(G)

# Determine if group is solvable: 
is_solvable(G)

# Nilpotency class: 
if is_nilpotent(G) nilpotency_class(G) end

# Degree: 
degree(G)

# Transitive number: 
transitive_group_identification(G)[2]

# Parity: 
is_even(G)

# Determine if group is primitive: 
is_primitive(G)

# Order of the centralizer of G in S_n: 
order(centralizer(symmetric_group(32), G)[1])

# Generators: 
gens(G)

# Conjugacy classes: 
conjugacy_classes(G)

# Character table: 
character_table(G)