  
  [1X4 [33X[0;0YExamples[133X[101X
  
  [33X[0;0YThe  following  examples  illustrate  the  use  of  [2XClassicalMaximalsGeneric[102X
  ([14X3.1-1[114X).[133X
  
  [33X[0;0YConsider  the  maximal  subgroups  of  [23X{\rm  SU}_5(7)[123X. These can be obtained
  directly as follows:[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27XL := ClassicalMaximalsGeneric("U", 5, 7);[127X[104X
    [4X[28X[ <matrix group of size 223883102951424 with 6 generators>,[128X[104X
    [4X[28X  <matrix group of size 32541148684800 with 6 generators>,[128X[104X
    [4X[28X  <matrix group of size 37298309529600 with 4 generators>,[128X[104X
    [4X[28X  <matrix group of size 15223799808 with 5 generators>,[128X[104X
    [4X[28X  <matrix group of size 491520 with 4 generators>,[128X[104X
    [4X[28X  <matrix group of size 10505 with 2 generators>,[128X[104X
    [4X[28X  <matrix group of size 276595200 with 4 generators>,[128X[104X
    [4X[28X  <matrix group of size 660 with 2 generators> ][128X[104X
    [4X[25Xgap>[125X [27XDefaultFieldOfMatrixGroup(L[1]);[127X[104X
    [4X[28XGF(7^2)[128X[104X
  [4X[32X[104X
  
  [33X[0;0YNote that unitary groups are defined over [23X\mathbb{F}_{q^2}[123X, even though they
  are parametrised by [23Xq[123X (see [14X2.2-3[114X).[133X
  
  [33X[0;0YIt  is often useful to restrict attention to certain Aschbacher classes. For
  example,  the  reducible  and imprimitive maximal subgroups of [23X{\rm Sp}_6(9)[123X
  (that  is,  classes [23X{\cal C}_1[123X and [23X{\cal C}_2[123X) can be obtained by specifying
  the optional argument [3Xclasses[103X:[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27XClassicalMaximalsGeneric("S", 6, 9, [1, 2]);[127X[104X
    [4X[28X[ <matrix group of size 1626546181017600 with 6 generators>,[128X[104X
    [4X[28X  <matrix group of size 19835929036800 with 6 generators>,[128X[104X
    [4X[28X  <matrix group of size 180506954234880 with 3 generators>,[128X[104X
    [4X[28X  <matrix group of size 2479113216000 with 4 generators>,[128X[104X
    [4X[28X  <matrix group of size 2239488000 with 4 generators>,[128X[104X
    [4X[28X  <matrix group of size 679311360 with 3 generators> ][128X[104X
  [4X[32X[104X
  
  [33X[0;0YThe  groups  returned  by  [2XClassicalMaximalsGeneric[102X  ([14X3.1-1[114X) are realised as
  subgroups  of  the  corresponding  standard  classical  group  and therefore
  preserve  the standard form. This can be verified using the stored invariant
  forms.  For  example,  consider a maximal subgroup of [23X{\rm \Omega}^-_8(5)[123X in
  class [23X{\cal C}_9[123X:[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27XG := ClassicalMaximalsGeneric("O-", 8, 5, [9])[1];[127X[104X
    [4X[28X<matrix group of size 372000 with 2 generators>[128X[104X
    [4X[25Xgap>[125X [27XDisplay(InvariantBilinearForm(G).matrix);[127X[104X
    [4X[28X . . . . . . . 1[128X[104X
    [4X[28X . . . . . . 1 .[128X[104X
    [4X[28X . . . . . 1 . .[128X[104X
    [4X[28X . . . 3 4 . . .[128X[104X
    [4X[28X . . . 4 1 . . .[128X[104X
    [4X[28X . . 1 . . . . .[128X[104X
    [4X[28X . 1 . . . . . .[128X[104X
    [4X[28X 1 . . . . . . .[128X[104X
    [4X[25Xgap>[125X [27XDisplay(InvariantBilinearForm(Omega(-1, 8, 5)).matrix);[127X[104X
    [4X[28X . . . . . . . 1[128X[104X
    [4X[28X . . . . . . 1 .[128X[104X
    [4X[28X . . . . . 1 . .[128X[104X
    [4X[28X . . . 3 4 . . .[128X[104X
    [4X[28X . . . 4 1 . . .[128X[104X
    [4X[28X . . 1 . . . . .[128X[104X
    [4X[28X . 1 . . . . . .[128X[104X
    [4X[28X 1 . . . . . . .[128X[104X
  [4X[32X[104X
  
  [33X[0;0YThe  two  matrices  coincide,  confirming  that  the  subgroup preserves our
  standard orthogonal form.[133X
  
