# Semidirect product of Z3 and D8 with action kernel V4

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 groupView a complete list of particular groups (this is a very huge list!)[SHOW MORE]

## Contents

## Definition

This group is defined by the following presentation:

## GAP implementation

### Group ID

This finite group has order 24 and has ID 8 among the groups of order 24 in GAP's SmallGroup library. For context, there are 15 groups of order 24. It can thus be defined using GAP's SmallGroup function as:

`SmallGroup(24,8)`

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

`gap> G := SmallGroup(24,8);`

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

`IdGroup(G) = [24,8]`

or just do:

`IdGroup(G)`

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

### Description by presentation

gap> F := FreeGroup(4); <free group on the generators [ f1, f2, f3, f4 ]> gap> G := F/[F.1^3,F.2^2,F.3^2,F.1*F.2*F.1^(-1)*F.2^(-1), F.1*F.3*F.1^(-1)*F.3^(-1), F.2*F.3*F.2^(-1)*F.3^(-1), F.4^2,F.4*F.1*F.4^(-1)*F.1,F.4*F.2*F.4^(-1)*F.3];