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1. The problem statement, all variables and given/known data

Show that every group of order (35)^3 has a normal subgroup of order 125.

2. Relevant equations

3. The attempt at a solution

I was trying to use the Third Sylow Theorem to show that there can only be one Sylow 5-subgroup but 21 Sylow 5-subgroups seems to work fine.

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# Homework Help: Group of order (35)^3

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