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
generated by
and
where ζ2n=e2πi/2n
is a primitive 2n-th root of unity.
x
:
Z
F
o
wr
Q
<