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That's a question I found in a french list of exercises online. I'm preparing myself for an exam, I think solving this question would really help. Thank you

The tip given by the exercise is to analyse the 7-Sylow.

I can't go any farther than $n_7=1$ or $8$ or $36$ or $288$.

Then I should analyse for each case.

I found similar questions online but couldn't quite understand the reasoning behind. They always show that the number of the Sylows can't be different than 1, which should show that the 7-Sylow is normal. The problem is that I can't understand how the usually get to show that $n_7=1$.

Would you please help me solve it or send maybe some papers about it or solved similar exercises?

Lucas Tonon
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  • Yeah, but that one is not complete and not very understandable in my opinion =(. Following the level of the questions of this same list of exercise I don't think it should be that complicated – Lucas Tonon Nov 03 '19 at 21:23
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    Perhaps I'm missing something, but it looks like the two answers together give a complete solution. If you want to avoid duplicating that question, I suggest editing this one to point to that question and then asking about the specific part of the argument you do not understand. – Travis Willse Nov 03 '19 at 21:25

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