Dicyclic group:Dic56

This article is about a particular group, i.e., a group unique upto isomorphism. View specific information (such as linear representation theory, subgroup structure) about this group
View a complete list of particular groups (this is a very huge list!)[SHOW MORE]

VIEW FACTS ABOUT THIS GROUP: All factsGroup property satisfactionsSubgroup property satisfactionsGroup property dissatisfactionsSubgroup property satisfactions
VIEW DEFINITIONS USING THIS AS EXAMPLE: All terms |Group properties |Subgroup properties|
VIEW FACTS USING THIS AS EXAMPLE: All facts |Group property non-implications |Subgroup property non-implications |Group metaproperty dissatisfactionsSubgroup metaproperty dissatisfactions

Definition

This group is defined as the dicyclic group of order $56$ (hence, degree $14$). In other words, it has the presentation:

$\langle a,b,c\mid a^{14}=b^{2}=c^{2}=abc\rangle$.

Arithmetic functions

Function	Value	Explanation
order	56
exponent	28

GAP implementation

Group ID

This finite group has order 56 and has ID 3 among the groups of order 56 in GAP's SmallGroup library. For context, there are groups of order 56. It can thus be defined using GAP's SmallGroup function as:

SmallGroup(56,3)

For instance, we can use the following assignment in GAP to create the group and name it $G$:

gap> G := SmallGroup(56,3);

Conversely, to check whether a given group $G$ is in fact the group we want, we can use GAP's IdGroup function:

IdGroup(G) = [56,3]

or just do:

IdGroup(G)

to have GAP output the group ID, that we can then compare to what we want.