# Direct product of SmallGroup(32,2) and Z2

From Groupprops

Revision as of 16:04, 3 September 2010 by Vipul (talk | contribs) (Created page with "{{particular group}} ==Definition== This group is defined as the external direct product of defining ingredient::SmallGroup(32,2) and [[defining ingredient::cyclic ...")

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]

## Definition

This group is defined as the external direct product of SmallGroup(32,2) and cyclic group:Z2.

## GAP implementation

### Group ID

This finite group has order 64 and has ID 56 among the groups of order 64 in GAP's SmallGroup library. For context, there are groups of order 64. It can thus be defined using GAP's SmallGroup function as:

`SmallGroup(64,56)`

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

`gap> G := SmallGroup(64,56);`

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

`IdGroup(G) = [64,56]`

or just do:

`IdGroup(G)`

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

### Other descriptions

Description | Functions used |
---|---|

DirectProduct(SmallGroup(32,2),CyclicGroup(2)) |
DirectProduct, SmallGroup, CyclicGroup |