Klein group

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The Klein group is a mathematical group defined by consisting of 4 elements each of one, but the identity, has order 2. It is abelian, and isomorphic to C2 × C2, the direct product of two copies of the cyclic group of order 2.

It has the following multiplication table:

oIabab
IIabab
aaIabb
bbabIa
ababbaI