  
  [1X3 [33X[0;0YConstruction of All Groups[133X[101X
  
  [33X[0;0YThe following function can be used to determine up to isomorphism all groups
  of  a given order. This method implements a combination of the more specific
  functions described below.[133X
  
  [33X[0;0YNote  that  the  chosen combination might not be the best possible for every
  application.  Thus, if this function takes too long to construct the desired
  groups,  then it might still be possible to determine these groups using the
  functions  outlined  in  the  following  chapters.  Moreover,  the functions
  described  in  the following chapters provide more facilities and this might
  help to determine groups with certain properties more efficiently.[133X
  
  
  [1X3.1 [33X[0;0YConstruction of All Groups[133X[101X
  
  [1X3.1-1 ConstructAllGroups[101X
  
  [33X[1;0Y[29X[2XConstructAllGroups[102X( [3Xorder[103X ) [32X function[133X
  
  [33X[0;0YUsually  the output of this function is a list of groups. The soluble groups
  in  the  list  are  given as pc groups and the others as permutation groups.
  However, in some cases the output might contain lists of groups as well. The
  groups  in  such a list could not be proved to be pairwise non-isomorphic by
  the  algorithm,  although this is likely to be the case, see Section [14X4.4[114X for
  further details.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27XConstructAllGroups( 60 );[127X[104X
    [4X[28X[ <pc group of size 60 with 4 generators>, [128X[104X
    [4X[28X  <pc group of size 60 with 4 generators>, [128X[104X
    [4X[28X  <pc group of size 60 with 4 generators>, [128X[104X
    [4X[28X  <pc group of size 60 with 4 generators>, [128X[104X
    [4X[28X  <pc group of size 60 with 4 generators>, [128X[104X
    [4X[28X  <pc group of size 60 with 4 generators>, [128X[104X
    [4X[28X  <pc group of size 60 with 4 generators>, [128X[104X
    [4X[28X  <pc group of size 60 with 4 generators>, [128X[104X
    [4X[28X  <pc group of size 60 with 4 generators>, [128X[104X
    [4X[28X  <pc group of size 60 with 4 generators>, [128X[104X
    [4X[28X  <pc group of size 60 with 4 generators>, [128X[104X
    [4X[28X  <pc group of size 60 with 4 generators>, A5 ][128X[104X
  [4X[32X[104X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27XList( last, IdGroup );[127X[104X
    [4X[28X[ [ 60, 4 ], [ 60, 13 ], [ 60, 6 ], [ 60, 2 ], [ 60, 1 ], [ 60, 7 ], [128X[104X
    [4X[28X  [ 60, 3 ], [ 60, 8 ], [ 60, 9 ], [ 60, 10 ], [ 60, 11 ], [ 60, 12 ], [128X[104X
    [4X[28X  [ 60, 5 ] ][128X[104X
  [4X[32X[104X
  
