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Groups and FieldsEasyThe Sylow Theorems

The Sylow Theorems · Easy problem

The dihedral group D11D_{11} (the 2222 symmetries of a regular 1111-gon) has order 22=2⋅1122 = 2\cdot11. Each of its 1111 reflections generates its own subgroup of order 22, and these are the only subgroups of order 22. How many Sylow 22-subgroups does D11D_{11} have?