The number N must be even. The group is the group generated by the composition of a rotation of angle 2pi/N with axis D and a plane symmetry P with P orthogonal to D.
Features
Algebraic structure: it is the cyclic group of order N
Kind of elements
N/2 elements: composition of rotation of angle (1+2k)2pi/N and plane symmetry P,
N/2 elements: rotation of angle k4pi/N with axis D.
Particular cases
if N=2, then the group is just one central symmetry and is denoted .
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