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<h1>1 Introduction</h1>

SglPPow is a package which extends the Small Groups Library. Currently the
Small Groups Library gives access to the following groups:


<dl compact>
<dt><var>(1)</var> <dd> Those of order at most 2000 except 1024 (423,164,062 groups);

<dt><var>(2)</var> <dd> Those of cubefree order at most 50,000 (395,703 groups);

<dt><var>(3)</var> <dd> Those of order p7 for the primes p=3,5,7,11 (907,489 groups);

<dt><var>(4)</var> <dd> Those of order pn for n ≤ 6 and all primes p;

<dt><var>(5)</var> <dd> Those of order pqn where qn divides 28, 36, 55 or 74 and
p is an arbitrary prime not equal to q;

<dt><var>(6)</var> <dd> Those of squarefree order;

<dt><var>(7)</var> <dd> Those whose order factorizes into at most 3 primes.
</dl>

This package gives access to the groups of order p7 for primes
p > 11, and to the groups of order 38.

To access the groups of order p7 for primes p > 11 you need the
packages LiePRing (by Michael Vaughan-Lee and Bettina Eick) and LieRing
(by Willem de Graaf and Serena Cicalo).

The groups of order 38 have been determined by Michael Vaughan-Lee.
The groups of order p7 for primes p > 11 are available via the
database of the nilpotent Lie rings of order pk for k ≤ 7 and
primes p > 3 in the LiePRing package. These groups are obtained from the
Lie rings using the implementation of the Baker-Campbell-Hausdorff formula
in the LieRing package.

<hr>Acknowledgements: The authors thank Max Horn for help with general
framework of GAP programs to extend the Small Groups Library.


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<address>sglppow manual March 2024
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