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\Chapter{Accessing the data}

When this package is loaded, then the groups of order $3^8$ and $p^7$ for 
$p > 11$ are additionally available via the SmallGroups library. As a result,
all groups of order $p^n$ with $p=2$ and $n \leq 9$ and $p=3$ and $n \leq 8$
and $p$ arbitrary and $n \leq 7$ 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 $3^8$, 1,600,573 groups of order $13^{7}$, and 5,546,909 groups
of order $17^7$. For general $p$ the number of groups of order $p^7$ is 
of order $3p^5$. Furthermore as $p$ increases, the time taken to
generate a complete list of the groups of order $p^7$ grows rapidly.
Experimentally the time seems to be proportional to $p^{6.2}$. 
For $p=13$ it
takes several hours to generate the complete list. For $p\leq 11$ 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 $13^7$ takes over 
11 gb of memory.

