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# Exercise 8.32
```{code-cell}
from itertools import permutations, product
from pprint import pformat
from numpy import zeros
from sympy.combinatorics.generators import symmetric
from IPython.display import Markdown
def display_symmetric(n: int):
perms = list(symmetric(n))
perm_dict = dict()
for i, perm in enumerate(perms):
perm_dict[i] = perm
inv_perms = {v: k for k, v in perm_dict.items()}
display(Markdown(f'**n = {n}**'))
print(pformat(perm_dict))
exp_table = zeros([len(perms), len(perms)], dtype=int)
conjugacy_table2 = zeros([len(perms), len(perms)], dtype=int)
for i, j in product(range(len(perms)), repeat=2):
a = perms[i]
b = perms[j]
exp_table[i, j] = inv_perms[a ^ b]
conjugacy_table2[i, j] = inv_perms[b * a * ~b]
display(Markdown('
exp_table'))
print(exp_table)
display(Markdown('
conjugacy_table2'))
print(conjugacy_table2)
[display_symmetric(n) for n in range(3,4)];
```