The Klein 4-group consists of three elements , and an identity . Every element is its own inverse, and the product of any two distinct non-identity elements is the remaining non-identity element. Thus the Klein 4-group admits the following elegant presentation: The Klein 4-group is isomorphic to . It is also the group of symmetries of a rectangle. It has three isomorphic subgroups, each of which is isomorphic to , and, of course, is normal, since the Klein 4-group is abelian.
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