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Jagat Chaudhary Best Answer
G, of order 1225=52×72 is abelian. By using Sylow's Theorem to show that we have two normal subgroups: one of order 49 and the other of order 25. Since the intersection of these subgroups must be 1, it follows that G is a direct product of these two subgroups. But subgroups of order p^2 are abelian, where p is a prime. Thus G is abelian. Keep asking, keep learning Jagat Chaudhary
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