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Groups and FieldsChallengeNormal Subgroups and Quotient Groups

Normal Subgroups and Quotient Groups · Challenge problem

In S4/V4S_4/V_4, where V4={e,(1 2)(3 4),(1 3)(2 4),(1 4)(2 3)}V_4=\{e,(1\,2)(3\,4),(1\,3)(2\,4),(1\,4)(2\,3)\}, how many cosets have order exactly 22?