Set bug in comparison of finite groups

[microncomputer]

Steps To Reproduce

Hi, I am using Set to check equality of groups by making Sets of the permutations. It should be true for all x 0-9 inclusive and gives true for 1-8 but false for 0 and 9 despite the fact that all the elements are there.

pete = graphs.PetersenGraph()
autpete = pete.automorphism_group()
pointstabilizers = [[g for g in autpete if g(x) == x] for x in pete.vertices()]

subgroup_check = [PermutationGroup(pointstabilizers[i]) for i in range(len(pointstabilizers))]

for i in range(10):
    print(Set(subgroup_check[i])  == Set(pointstabilizers[i]), all([u in Set(subgroup_check[i]) for u in Set(pointstabilizers[i])]))

returns

False True
True True
True True
True True
True True
True True
True True
True True
True True
False True

Expected Behavior

equality

Actual Behavior

only sometimes

Additional Information

No response

Environment

• OS: WSL2 ubuntu 22
• Sage Version: 10.4

Checklist

• I have searched the existing issues for a bug report that matches the one I want to file, without success.
• I have read the documentation and troubleshoot guide

[maxale]

I'm not sure if Set should be blamed here. Elements of pointstabilizers[0] and subgroup_check[0] have different parents:

print( pointstabilizers[0][0].parent() )
print( subgroup_check[0][0].parent() )

tell us

Permutation Group with generators [(3,7)(4,5)(8,9), (1,4,5)(2,3,8,6,9,7), (0,1,2,3,8,5)(4,6,7)]
Permutation Group with generators [(), (3,7)(4,5)(8,9), (2,6)(3,8)(4,5)(7,9), (2,6)(3,9)(7,8), (1,4)(2,3)(6,9)(7,8), (1,4,5)(2,3,8,6,9,7), (1,4)(2,9)(3,6), (1,4,5)(2,9,8)(3,7,6), (1,5,4)(2,7,9,6,8,3), (1,5)(2,7)(3,9)(6,8), (1,5)(2,8)(6,7), (1,5,4)(2,8,9)(3,6,7)]

A possible solution is to convert elements of subgroup_check[0] to the parent of pointstabilizers[0], which is autpete - like this:

Set(pointstabilizers[0]) == Set(map(autpete,subgroup_check[0]))