SO(5)

In mathematics, SO(5), also denoted SO5(R) or SO(5,R), is the special orthogonal group of degree 5 over the field R of real numbers, i.e. (isomorphic to) the group of orthogonal 5×5 matrices of determinant 1.
Geometric interpretation.
SO(5) is a subgroup of the direct Euclidean group "E"+(5), the group of "direct" isometries, i.e., isometries preserving orientation, of R5, consisting of elements which leave the origin fixed.
More precisely, we have:
where "T" is the translational group of R5.
Lie group.
SO(5) is a simple Lie group of dimension 10.