General affine group:GA(1,7)
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The group is defined in the following equivalent ways:
- It is the holomorph of the cyclic group of order seven.
- it is the general affine group of degree one over the field of seven elements.
|minimum size of generating set||2|
This finite group has order 42 and has ID 1 among the groups of order 42 in GAP's SmallGroup library. For context, there are groups of order 42. 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(42,1);
Conversely, to check whether a given group is in fact the group we want, we can use GAP's IdGroup function:
IdGroup(G) = [42,1]
or just do:
to have GAP output the group ID, that we can then compare to what we want.