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Groups and FieldsMediumNormal Subgroups and Quotient Groups

Normal Subgroups and Quotient Groups · Medium problem

In Z60\mathbb Z_{60}, let H=⟨6⟩H = \langle 6\rangle (order 1010) and N=⟨10⟩N = \langle 10\rangle (order 66). Using the Second Isomorphism Theorem relation ∣HN∣=∣H∣∣N∣∣H∩N∣|HN| = \dfrac{|H||N|}{|H\cap N|}, what is ∣HN∣|HN|?