Its group of conformal transformations is none other than 'G'.
There is a group of transformations in one space and one time dimension for which this operation forms the addition law.
More formally, it is the group of transformations that preserve the conformal geometry of the space.
It is also the group of determinant-preserving linear transformations of the exceptional Jordan algebra.
Geometry is the study of shapes and space, in particular, groups of transformations that act on spaces.
Thus geometries would be classified by groups of transformations which left certain geometrical aspects invariant.
Formally, its group of conformal transformations is infinite dimensional.
One notes that the Erlangen program attempted to identify invariants under a group of transformations.
They went on to investigate W-curves, curves invariant under a group of projective transformations.
The metric is invariant under the group of quaplectic transformations.
