  
  [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 Neubüser [FN68], [FN70], whose algorithm used the output of their
  subgroup  lattice  program.  A  technique developed by Neubüser 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  [Hul96]  in the [5XGAP[105X 4 library. Cannon and Holt
  [CH03] 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
  [Sho28],  Hulpke  in  1997 implemented a practical method for finite abelian
  groups in the [5XGAP[105X 4 library. Wursthorn [Wur93] 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 [Smi94] 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  [New77] and O'Brien
  [O'B90]  can  be  modified  to  compute  the  automorphism group of a finite
  [22Xp[122X-group  as outlined in [O'B95]. 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,  described  in  [ELO02],  is a
  refinement  of  the  methods  described  in  [O'B95].  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
  
