General affine group:GA(1,8)
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 group
View a complete list of particular groups (this is a very huge list!)[SHOW MORE]
This group is defined as the general affine group of degree one over the field of eight elements. In other words, it is the semidirect product of the additive group of this field and the multiplicative group of the field.
|minimum size of generating set||2|
This finite group has order 56 and has ID 11 among the groups of order 56 in GAP's SmallGroup library. For context, there are 13 groups of order 56. It can thus be defined using GAP's SmallGroup function as:
For instance, we can use the following assignment in GAP to create the group and name it :
gap> G := SmallGroup(56,11);
Conversely, to check whether a given group is in fact the group we want, we can use GAP's IdGroup function:
IdGroup(G) = [56,11]
or just do:
to have GAP output the group ID, that we can then compare to what we want.