 Special orthogonal group

The special orthogonal group isEvery element of $SO(2)$ is a rotation in the plane. Every element of $SO(3)$ fixes an axis and restricts to a planar rotation on its perpendicular plane.

Group of rotations of a rigid body.

Like orthogonal group but without reflections. So it is a "special case" of the orthogonal group.

This is a subgroup of both the orthogonal group and the special linear group.