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GrpConst

Constructing the Groups of a Given Order

2.7.0

14 August 2026

Hans Ulrich Besche

Bettina Eick
Email: beick@tu-bs.de
Homepage: http://www.iaa.tu-bs.de/beick
Address:
Institut Analysis und Algebra
TU Braunschweig
Universitätsplatz 2
D-38106 Braunschweig
Germany

1 Preface

2 Introduction to GrpConst

3 Construction of All Groups

3.1 Construction of All Groups

3.1-1 ConstructAllGroups

4 The Frattini Extension Method

4.1 The Main Frattini Extension Function

4.1-1 FrattiniExtensionMethod

4.2 The Construction of Frattini Free Groups

4.2-1 FrattiniFactorCandidates

4.3 The Determination of Frattini Extensions

4.3-1 FrattiniExtensions

4.4 Verifying non-isomorphism

4.4-1 DistinguishGroups

5 The Cyclic Split Extension Method

5.1 The Main Function

5.1-1 CyclicSplitExtensionMethod

5.2 The Underlying Functions

5.2-1 CyclicSplitExtensions
5.2-2 CyclicSplitExtensionsUp

6 The Upwards Extension Method

6.1 The Upwards Extension Method

  6.1-1 UpwardsExtensions
  6.1-2 CyclicExtensions
  6.1-3 UpwardsExtensionsNoCentre
  6.1-4 ExtensionsByGroupNoCentre

7 Examples with Runtimes

References

Index

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