UCLA Abstract Algebra Prove a Group with Order 648 Is Not Simple Discussion

Description

Requirements: I would like a rigorous proof that cites all theorems used proving that a group of order 648 cannot be a simple group. It is important to only use methods from undergraduate abstract algebra as this question is for a review for my upcoming midterm, and I need to be able to solve questions like this using information already gone over.With this in mind, there is a hint attached reading:Hint: consider the possibilities for n3, and the conjugation action of G on Syl3(G)
Ideally the proof used will revolve around this idea.

Tags:
Abstract Algebra

conjugation

permutation

simple group

order 648 group

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