General affine group:GA(2,3)
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Contents
Definition
This group is defined in the following equivalent ways:
- It is the general affine group of degree two over field:F3.
- It is the holomorph of elementary abelian group:E9.
Arithmetic functions
Function | Value | Similar groups | Explanation |
---|---|---|---|
order (number of elements, equivalently, cardinality or size of underlying set) | 432 | groups with same order | As : |
number of conjugacy classes | 11 | groups with same order and number of conjugacy classes | groups with same number of conjugacy classes | As : |
GAP implementation
Group ID
This finite group has order 432 and has ID 734 among the groups of order 432 in GAP's SmallGroup library. For context, there are 775 groups of order 432. It can thus be defined using GAP's SmallGroup function as:
SmallGroup(432,734)
For instance, we can use the following assignment in GAP to create the group and name it :
gap> G := SmallGroup(432,734);
Conversely, to check whether a given group is in fact the group we want, we can use GAP's IdGroup function:
IdGroup(G) = [432,734]
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 |
---|---|
Holomorph(ElementaryAbelianGroup(9)) | Holomorph (not an in-built GAP command), ElementaryAbelianGroup |