[sglppow] 2 Accessing the data

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# 2 Accessing the data

When this package is loaded, then the groups of order 38 and p7 for p > 11 are additionally available via the SmallGroups library. As a result, all groups of order pn with p=2 and n ≤9 and p=3 and n ≤8 and p arbitrary and n ≤7 are then available via the small groups library. The corresponding information can be obtained via

- `SmallGroup(size, number)`

- `NumberSmallGroups(size)`

- `SmallGroupsInformation(size)`

  There is no IdGroup function available for this extension of the small groups library.

  WARNING: The user should be aware that there are there are 1,396,077 groups of order 38, 1,600,573 groups of order 137, and 5,546,909 groups of order 177. For general p the number of groups of order p7 is of order 3p5. Furthermore as p increases, the time taken to generate a complete list of the groups of order p7 grows rapidly. For p=13 it takes several hours to generate the complete list. For p≤11 the groups are precomputed, and their SmallGroup codes are stored in the SmallGroups database. For p>11 the Lie rings have to be generated from 4773 parametrized presentations in the LiePRing database, and then converted into groups using the Baker-Campbell-Hausdorff formula. A complete list of power commutator presentations for the groups of order 137 takes over 11 gb of memory.

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