# Dihedral group

From Groupprops

WARNING: POTENTIAL TERMINOLOGICAL CONFUSION: Please don't confuse this with dicyclic group (also called binary dihedral group)

This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism

View a complete list of group propertiesVIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions

*This is a family of groups parametrized by the natural numbers, viz, for each natural number, there is a unique group (upto isomorphism) in the family corresponding to the natural number. The natural number is termed the parameter for the group family*

This article is about a general term. A list of important particular cases (instances) is available at Category:Dihedral groups

## Definition

The **dihedral group** with parameter , denoted sometimes as and sometimes as is defined in the following equivalent ways:

- It has the presentation:

- It is the group of symmetries of a regular -gon in the plane, viz the plane isometries that preserves the set of points of the regular -gon.