Properties
For each n > 1, the dicyclic group Dicn is a non-abelian group of order 4n. ("Dic1" is C4, the cyclic group of order 4, which is abelian, and is not considered dicyclic.)
Let A = <a> be the subgroup of Dicn generated by a. Then A is a cyclic group of order 2n, so = 2. As a subgroup of index 2 it is automatically a normal subgroup. The quotient group Dicn/A is a cyclic group of order 2.
Dicn is solvable; note that A is normal, and being abelian, is itself solvable.
Read more about this topic: Dicyclic Group
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