Dicyclic groups Dicn
Dicyclic or binary dihedral group Dicn is a group of order 4n,
which the unique non-split extension C2n.C2 with C2
acting by -1.
(The split extension in this case is the dihedral group.)
Alternatively, it is a split extension
with action by -1 in both cases. It can be realised as a group of complex matrices
is a primitive 2n-th root of unity.