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1 Introduction

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

1. Those of order at most 2000 except 1024 (423,164,062 groups);

2. Those of cubefree order at most 50,000 (395,703 groups);

3. Those of order p^7 for the primes p=3,5,7,11 (907,489 groups);

4. Those of order p^n for n≤ 6 and all primes p;

5. Those of order pq^n where q^n divides 2^8, 3^6, 5^5 or 7^4 and p is an arbitrary prime not equal to q;

6. Those of squarefree order;

7. Those whose order factorizes into at most 3 primes.

This package gives access to the groups of order p^7 for primes p>11, and to the groups of order 3^8.

To access the groups of order p^7 for primes p>11 you need the packages LiePRing (by Michael Vaughan-Lee and Bettina Eick) and LieRing (by Willem de Graaf and Serena Cicalò).

The groups of order 3^8 have been determined by Michael Vaughan-Lee. The groups of order p^7 for primes p>11 are available via the database of the nilpotent Lie rings of order p^k 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.

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

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