* It is the group comprising the elements <math>(\pm 1, \pm 1)</math> under coordinate-wise multiplication
* It is the unique non-cyclic group of order 4
* It is the subgroup of [[symmetric group:S4|the symmetric group of
degre four]] comprising the double transpositions, and the identity element.* It is the [[Burnside group]] <math>B(2,2)</math>: the ''free group'' on two generators with exponent two.