  
  [1X2 [33X[0;0YIntroduction to GrpConst[133X[101X
  
  [33X[0;0YThis  package  contains  three  methods to construct the groups of a certain
  type up to isomorphism.[133X
  
  [33X[0;0Y[13XThe Frattini Extension Method[113X:[133X
  
  [33X[0;0YThis  method  can  be used to determine all soluble groups of a given order.
  The  practicability  of  the  method  depends  clearly  on the chosen order.
  Furthermore,  the efficiency of the method might be increased by restricting
  the  construction to groups with certain properties. This is easily possible
  for a number of properties; for example, it is useful and straightforward to
  compute non-nilpotent groups only. (See Chapter [14X4[114X.)[133X
  
  [33X[0;0Y[13XThe Cyclic Split Extension Method[113X:[133X
  
  [33X[0;0YThe  cyclic  split  extension method can be used to list all groups of order
  [22Xp^n  ⋅  q[122X  for  different primes [22Xp[122X and [22Xq[122X which have a normal Sylow subgroup.
  These  groups  are  also  soluble,  and  hence might also be obtained by the
  Frattini  extension  method.  However,  the cyclic split extension method is
  more  effective  in  this  case.  Note  that this method relies on a list of
  groups  of  order [22Xp^n[122X. Moreover, the efficiency of this method depends on an
  effective  method  to  compute automorphism groups of [22Xp[122X-groups. (See Chapter
  [14X5[114X.)[133X
  
  [33X[0;0Y[13XThe Upwards Extension Method[113X:[133X
  
  [33X[0;0YThe  upwards  extension  method is the most general of the three methods. It
  can  be  used  to  construct all groups of a given order. However, it is the
  least  efficient  of  the  three  methods  and  hence should only be used to
  construct  non-soluble groups. Note that this method needs a list of perfect
  groups of order dividing the given one. (See Chapter [14X6[114X.)[133X
  
  [33X[0;0YFurthermore,  the  package  contains  a  wrap-up function which combines the
  three  methods  into  a general algorithm to construct the groups of a given
  order. (See Chapter [14X3[114X.) Finally, there is an info class [10XInfoGrpCon[110X available
  for the functions of this package with possible levels 1 up to 4.[133X
  
