A symmetry group is a mathematical concept that describes the set of all symmetries of a given object. These symmetries include transformations such as rotations, reflections, and translations that leave the object's structure unchanged. Symmetry groups are essential in various fields, including geometry, physics, and chemistry, as they help classify and analyze the properties of shapes and patterns. In group theory, a symmetry group is defined as a collection of these transformations that can be combined through specific operations, forming a group. Each symmetry can be represented mathematically, allowing for a deeper understanding of the object's characteristics. Examples of symmetry groups include the dihedral group for polygons and the rotation group for three-dimensional objects.