Dicyclic groups Dic_n

Dicyclic or binary dihedral group Dic_n is a group of order 4n, which the unique non-split extension C_2n.C₂ with C₂ acting by -1. (The split extension in this case is the dihedral group.) Alternatively, it is a split extension

odd n	Dic_n=C_n⋊C₄
even n=2^km	Dic_n=C_m⋊Q_2^k+2

with action by -1 in both cases. It can be realised as a group of complex matrices generated by

ζ_2n	0
0	ζ_2n^-1

and

0	-1
1	0

where ζ_2n=e^2πi/2n is a primitive 2n-th root of unity.

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Dicyclic groups Dicn

Dicyclic groups Dic_n