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Cubefree

Constructing the Groups of a Given Cubefree Order

1.22

6 August 2026

Heiko Dietrich
Email: heiko.dietrich@monash.edu
Homepage: http://users.monash.edu.au/~heikod/
Address:
School of Mathematical SciencesMonash University
VIC 3800
Melbourne, Australia

Contents

1 Introduction
 1.1 Overview
 1.2 Theoretical background
2 Functionality of the Cubefree package
 2.1 New methods

  2.1-1 ConstructAllCFGroups
  2.1-2 ConstructAllCFSolvableGroups
  2.1-3 ConstructAllCFNilpotentGroups
  2.1-4 ConstructAllCFSimpleGroups
  2.1-5 ConstructAllCFFrattiniFreeGroups
  2.1-6 IsomorphismCubefreeGroups
  2.1-7 IsIsomorphicCubefreeGroups
  2.1-8 NumberCFGroups
  2.1-9 NumberCFSolvableGroups
  2.1-10 CountAllCFGroupsUpTo
  2.1-11 CubefreeOrderInfo
  2.1-12 CubefreeTestOrder
  2.1-13 IsCubeFreeInt
  2.1-14 IsSquareFreeInt
  2.1-15 IrreducibleSubgroupsOfGL
  2.1-16 RewriteAbsolutelyIrreducibleMatrixGroup
 2.2 Comments on the implementation
 2.3 Comments on the efficiency
 2.4 An example session
 2.5 Accuracy check
3 Installing and loading the Cubefree package
 3.1 Installing the Cubefree package
 3.2 Loading the Cubefree package
References
Index

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