Groupprops, The Group Properties Wiki (pre-alpha)
Take a short survey about Math Resources on the Internet.

From Groupprops

This article is about a particular group, viz a group unique upto isomorphism[SHOW MORE]

View a complete list of particular groups

Contents 1 Definition 2 GAP implementation 2.1 Group ID 2.2 Other descriptions

Definition

The direct product of M16 and Z2 is defined as the group obtained as the external direct product of the group M16 and the cyclic group of order two.

GAP implementation

Group ID

This finite group has order 32 and has ID 37 among the group of order 32 in GAP's SmallGroup library. It can thus be defined using GAP's SmallGroup function as:

SmallGroup(32,37)

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

gap> G := SmallGroup(32,37);

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

IdGroup(G) = [32,37]

or just do:

IdGroup(G)

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

Other descriptions

The group can be described using the DirectProduct, SmallGroup, and [{GAP:CyclicGroup|CyclicGroup]] functions:

DirectProduct(SmallGroup(16,6),CyclicGroup(2))