Rotation
C_{n}
If rotation through an angle of 360°/n about an axis of symmetry leaves the molecule in an indistinguishable condition, it is said to have an nfold axis of symmetry. The presence of this element is denoted as C_{n}.
If the molecule is rotated k times through 2π/n, C_{n}^{k} indicates this operation. If C_{n} is applied n times, the molecule is again in the initial position, i.e. C_{n}^{n}≡ E.
Example: Water C_{2} (Movie,
694kB)
We can imagine the molecule H_{2}O being turned through any angle about the bisecting line of the angle HOH, but only a rotation of 180°,
(C_{2} ) yields an image which is indistinguishable from the original. In contrast, if the same operation is applied to HOD, the molecule displays another orientation.
Example: Ammonia C_{3} (Movie, 455kB)
The trigonal pyramidal molecule NH_{3} possesses a threefold rotational axis running through the centre of the nonbonding orbital, the nucleus of N and the plane spanned by the three hydrogen atoms.
The rotational axis C_{3} is centre for two operations. One is a rotation through 120° and the other about two times this angle, the operations are denoted C_{3} and C_{3}^{2}. It is not necessary to discuss a rotation by three times 120° as this operations equals identity. 
Example: Benzene (C_{6} , C_{2} )
Benzene displays six axes C_{2} within the plane of the molecule and the centre of symmetry and, in addition, perpendicular to this plane, a sixfold axis C_{6} running as well through the centre of symmetry. The axis which produces a maximal number of identical images within one complete turn, or, in other words, with maximal n, is said to be the principal axis 
Example: Hydrogen cyanide C_{∞}

In linear molecules like hydrogen cyanide, there is always an infinitefold rotational axis C_{∞} which is identical to what usually is regarded as the molecules' axis. 
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