Open main menu

Groupprops β

Direct product of A4 and D8

Definition

This group is defined as the external direct product of alternating group:A4 and dihedral group:D8.

Arithmetic functions

GAP implementation

Group ID

This finite group has order 96 and has ID 197 among the groups of order 96 in GAP's SmallGroup library. For context, there are 231 groups of order 96. It can thus be defined using GAP's SmallGroup function as:

SmallGroup(96,197)

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

gap> G := SmallGroup(96,197);

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

IdGroup(G) = [96,197]

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(AlternatingGroup(4),DihedralGroup(8)) DirectProduct, AlternatingGroup, DihedralGroup