Normal modes can be computed by stepping through a descending sequence of one type of these objects via successive atom substitutions, and reading a correlation table. Volume A of the International Tables for Crystallography is a list of one type of these objects. Mulliken symbols like A1 and B2 (-5[1])are used to label the rows of 2D diagrams whose columns correspond to elements of these objects. S·A·L·Cs transform with the irreps of these objects. Whether a molecule is IR or Raman-active can be read from the (*) character table for one of these objects. Examples of these (10[1])objects like C-sub-infinity and T-sub-d respectively describe linear and tetrahedral molecules, and are built up from elements like axes of rotation and planes of reflection. For 10 points, “point” examples of what algebraic objects describe the symmetries of molecules? ■END■ (10[2])