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Groups and FieldsEasyCosets and Lagrange's Theorem

Cosets and Lagrange's Theorem · Easy problem

In S4S_4 (order 2424), let H={e,(12)(34),(13)(24),(14)(23)}H = \{e, (12)(34), (13)(24), (14)(23)\}, a subgroup of order 44. Since the left cosets of HH partition S4S_4, how many elements of S4S_4 lie outside HH?