📚 Description

This is a review PR for #35540.

(1) It adds a test in the centralizer method in GroupMixinLibGAP.
(2) It changes a variable name centralizer -> centralizer_gens in the centralizer method
(3) It adds the group_id method in GroupMixinLibGAP.

For (2), the variable does not represent the centralizer, but a set of generators.

📝 Checklist

• The title is concise, informative, and self-explanatory.
• The description explains in detail what this PR is about.
• I have linked a relevant issue or discussion.
• I have created tests covering the changes.
• [x ] I have updated the documentation accordingly.

⌛ Dependencies

#35540: This is a review PR for that #35540.