  
  
                              [1X ClassicalMaximals [101X
  
  
                    [1X Maximal subgroups of classical groups [101X
  
  
                                      1.1
  
  
                                  26 May 2026
  
  
                                Maximilian Hauck
  
                                    Max Horn
  
                               Tristan Pfersdorff
  
                                Christian Seeger
  
                                 Sergio Siccha
  
  
  
  Maximilian Hauck
      Email:    [7Xmailto:mahauck@rhrk.uni-kl.de[107X
  Max Horn
      Email:    [7Xmailto:mhorn@rptu.de[107X
  Tristan Pfersdorff
      Email:    [7Xmailto:tristan.pfersdorff@edu.rptu.de[107X
  Christian Seeger
      Email:    [7Xmailto:christian.seeger@edu.rptu.de[107X
  Sergio Siccha
      Email:    [7Xmailto:siccha@mathematik.uni-kl.de[107X
  
  -------------------------------------------------------
  
  
  [1XContents (ClassicalMaximals)[101X
  
  1 [33X[0;0YIntroduction[133X
    1.1 [33X[0;0YPhilosophy[133X
    1.2 [33X[0;0YOverview over this manual[133X
    1.3 [33X[0;0YFeedback and Support[133X
    1.4 [33X[0;0YFunding[133X
  2 [33X[0;0YClassical Groups and Aschbacher's Theorem[133X
    2.1 [33X[0;0YClassical Forms[133X
      2.1-1 [33X[0;0YSesquilinear forms[133X
      2.1-2 [33X[0;0YQuadratic forms[133X
      2.1-3 [33X[0;0YMatrix realizations of classical forms[133X
      2.1-4 [33X[0;0YNon-degeneracy[133X
      2.1-5 [33X[0;0YIsometries and similarities[133X
      2.1-6 [33X[0;0YClassification of sesquilinear forms[133X
    2.2 [33X[0;0YClassical Groups[133X
      2.2-1 [33X[0;0YLinear Groups (Case [22XL[122X)[133X
      2.2-2 [33X[0;0YSymplectic Groups (Case [22XS[122X)[133X
      2.2-3 [33X[0;0YUnitary Groups (Case [22XU[122X)[133X
      2.2-4 [33X[0;0YOrthogonal groups in odd dimension (Case [22XO[122X)[133X
      2.2-5 [33X[0;0YOrthogonal groups in even dimension (Cases [22XO^+[122X and [22XO^-[122X)[133X
      2.2-6 [33X[0;0YStandard forms in [5XClassicalMaximals[105X[133X
    2.3 [33X[0;0YAschbacher's Theorem[133X
  3 [33X[0;0YMaximal Subgroups of Classical Groups[133X
    3.1 [33X[0;0YThe Main function[133X
      3.1-1 ClassicalMaximalsGeneric
    3.2 [33X[0;0YConjugating elements in the ambient classical group[133X
      3.2-1 GLMinusSL
      3.2-2 GUMinusSU
      3.2-3 NormSpMinusSp
      3.2-4 SOMinusOmega
      3.2-5 GOMinusSO
      3.2-6 NormGOMinusGO
      3.2-7 [33X[0;0YWarning concerning orthogonal groups of minus type[133X
  4 [33X[0;0YExamples[133X
  5 [33X[0;0YUtility Functions[133X
    5.1 [33X[0;0YMatrix Functions[133X
      5.1-1 MatrixByEntries
      5.1-2 AntidiagonalMat
      5.1-3 AntidiagonalHalfOneMat
      5.1-4 RotateMat
    5.2 [33X[0;0YCreating Matrix Groups[133X
      5.2-1 MatrixGroup
      5.2-2 MatrixGroupWithSize
    5.3 [33X[0;0YSpecial generators for classical groups[133X
      5.3-1 GeneratorsOfOrthogonalGroup
      5.3-2 StandardGeneratorsOfOrthogonalGroup
      5.3-3 AlternativeGeneratorsOfOrthogonalGroup
      5.3-4 StandardGeneratorsOfLinearGroup
    5.4 [33X[0;0YSizes of classical groups[133X
      5.4-1 SizeSp
      5.4-2 SizePSp
      5.4-3 SizeSU
      5.4-4 SizePSU
      5.4-5 SizeGU
      5.4-6 SizeGO
      5.4-7 SizeSO
      5.4-8 SizeOmega
  
  
  [32X
