Unitriangular matrix group:UT(3,7)
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This group is defined in the following equivalent ways:
- It is the unitriangular matrix group of degree three over field:F7. In other words, it is the group UT(3,p) for .
- It is the unique non-abelian group of order and exponent .
- It is the extraspecial group of order .
This finite group has order 343 and has ID 3 among the groups of order 343 in GAP's SmallGroup library. For context, there are groups of order 343. 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(343,3);
Conversely, to check whether a given group is in fact the group we want, we can use GAP's IdGroup function:
IdGroup(G) = [343,3]
or just do:
to have GAP output the group ID, that we can then compare to what we want.