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:
| o | I | a | b | ab |
|---|---|---|---|---|
| I | I | a | b | ab |
| a | a | I | ab | b |
| b | b | ab | I | a |
| ab | ab | b | a | I |