Step 108

The complete set of all symmetry operations executable at a given molecule (movements, which transfer the molecule into an arrangement indistinguishable in relation to the output arrangement) forms a mathematical group.

These groups are called point groups of symmetry, since with the symmetry operations regarded by us at least in each case one point remains invariant, i.e. its position in the space does not modify. (exactly one point remains invariant with inversions and rotational reflexion; when turns a whole straight line remains invariant and with reflections a whole level.) In contrast to it there are the space groups occurring with crystals, with which no point remains invariant. We offer now two program ways to you: The first way leads directly to the determination of the groups of points of symmetry, without dealing with group-theoretical aspects more in greater detail, the other one gives first a detailed explanation of the control break item.

Without group theory it continues here !

With group theory it continues here !