  
  [1X1 [33X[0;0YIntroduction[133X[101X
  
  
  [1X1.1 [33X[0;0YIntroduction[133X[101X
  
  [33X[0;0YGiven  an  arbitrary finite group, the computation of its automorphism group
  is  a  very  difficult  task.  Pioneer  work in this area was carried out by
  Felsch  and  Neubueser  (1970),  whose  algorithm  used  the output of their
  subgroup  lattice  program.  A technique developed by Neubueser in the early
  1970s sought to compute the automorphism group viewed as a permutation group
  acting on unions of certain conjugacy classes of the group. A similar method
  was  implemented by Hulpke (1997) in the [5XGAP[105X 4 library. Recently, Cannon and
  Holt (1999) presented a new algorithm which uses a [13Xhybrid group[113X approach.[133X
  
  [33X[0;0YMore  efficient approaches are available to determine the automorphism group
  for  groups  satisfying  certain  properties.  Following  the  work of Shoda
  (1928),  Hulpke  in  1997  implemented a practical method for finite abelian
  groups  in the [5XGAP[105X 4 library. Wursthorn (1993) adapted modular group algebra
  techniques  to  compute the automorphism groups of [22Xp[122X-groups; the [5XGAP[105X 3 share
  package  [5XSisyphos[105X  includes  an  implementation.  Smith (1994) introduced an
  algorithm  for  finite solvable groups which is available in the [5XAutAg[105X share
  package of [5XGAP[105X 3.[133X
  
  [33X[0;0YMoreover,  the [22Xp[122X-group generation method of Newman (1977) and O'Brien (1990)
  can  be  modified  to  compute the automorphism group of a finite [22Xp[122X-group as
  outlined  in  O'Brien  (1995). This algorithm is implemented in the ANU [10Xpq[110X C
  program.[133X
  
  [33X[0;0YHere  we  introduce  a  new  function to compute the automorphism group of a
  finite  [22Xp[122X-group.  The  underlying  algorithm  is a refinement of the methods
  described  in  O'Brien  (1995).  In  particular, this implementation is more
  efficient in both time and space requirements and hence has a wider range of
  applications  than the ANU [10Xpq[110X method. Our package is written in [5XGAP[105X code and
  it makes use of a number of methods from the [5XGAP[105X library such as the MeatAxe
  for matrix groups and permutation group functions.[133X
  
  [33X[0;0YThe  [5XGAP[105X 4 package [5XANUPQ[105X, which is an interface to most of the functionality
  of  the  ANU  [10Xpq[110X C program, uses the [5XAutPGrp[105X package to compute automorphism
  groups of [22Xp[122X-groups.[133X
  
  [33X[0;0YWe  have  compared  our  method  to the others available in [5XGAP[105X. Our package
  usually  out-performs all but the method designed for finite abelian groups.
  We  note  that our method uses the small groups library in certain cases and
  hence  our  algorithm  is  more  effective  if  the  small groups library is
  installed.[133X
  
