Finite groups · Family
Dicyclic groups
Dicₙ has order 4n; Dic₂ = Q₈ and Dic₄ = Q₁₆.
Reference coverageFinite families
Parameter domain
Dicₙ has order 4n; Dic₂ = Q₈ and Dic₄ = Q₁₆.
| Parameter | Allowed values |
|---|---|
| n | integer n ≥ 2 |
Reference properties
Conventions and use
For n a power of two this is a generalized quaternion group. [sources]
Names and aliases
Binary dihedral groups
Claims and sources
Each assertion has a stable identifier within this record and a source locator or derivation. Cite the dataset edition when referring to a corrected or historical claim.
Definition
The group with a^(2n) = 1, x² = aⁿ and xax⁻¹ = a⁻¹.
- GAP Reference Manual: Group LibrariesSections 50.1-8 DicyclicGroup and 50.1-9 IsDicyclicGroupOpen source
family:finite-dicyclic#definitionParameter domain
n: integer n ≥ 2
- GAP Reference Manual: Group LibrariesSections 50.1-8 DicyclicGroup and 50.1-9 IsDicyclicGroupOpen source
family:finite-dicyclic#parametersScope and restrictions
Dicₙ has order 4n; Dic₂ = Q₈ and Dic₄ = Q₁₆.
- GAP Reference Manual: Group LibrariesSections 50.1-8 DicyclicGroup and 50.1-9 IsDicyclicGroupOpen source
family:finite-dicyclic#restrictionConventions and use
For n a power of two this is a generalized quaternion group.
- GAP Reference Manual: Group LibrariesSections 50.1-8 DicyclicGroup and 50.1-9 IsDicyclicGroupOpen source
family:finite-dicyclic#conventions-1