Klein four-group
In mathematics, the Klein four-group (or Viergruppe), named after Felix Klein is the smallest non-cyclic group. It has 4 elements, all but the identity having order 2. It is abelian, and is isomorphic to C2 × C2, the direct product of two copies of the cyclic group of order 2.
It has the following multiplication table:
| 1 | a | b | ab | |
|---|---|---|---|---|
| 1 | 1 | a | b | ab |
| a | a | 1 | ab | b |
| b | b | ab | 1 | a |
| ab | ab | b | a | 1 |