Dicyclic group:Dic28

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Definition

This group is defined as the dicyclic group of order $28$ (hence, degree $7$). In other words, it has the presentation:

$\langle a,b,c\mid a^{7}=b^{2}=c^{2}=abc\rangle$.

Arithmetic functions

Function	Value	Explanation
order	28
exponent	28
derived length	2

GAP implementation

Group ID

This finite group has order 28 and has ID 1 among the groups of order 28 in GAP's SmallGroup library. For context, there are groups of order 28. It can thus be defined using GAP's SmallGroup function as:

SmallGroup(28,1)

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

gap> G := SmallGroup(28,1);

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

IdGroup(G) = [28,1]

or just do:

IdGroup(G)

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