A group is metacyclic when it has a cyclic normal subgroup whose quotient is cyclic. Every dihedral group is metacyclic through its rotation subgroup.
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A metacyclic group is a specific type of group in group theory, which is a branch of mathematics. More precisely, it is a particular kind of solvable group that has a structure related to cyclic groups. A group \( G \) is called metacyclic if it has a normal subgroup \( N \) that is cyclic, and the quotient group \( G/N \) is also cyclic.