62.72 Automorphisms for groups

Automorphisms( group )

Automorphisms computes all the automorphisms of the group group. The automorphisms are returned as a list of transformations s.t. the identity automorphism is always the last entry in this list. For each transformation in this list the record components is-Group-En-do-mor-phism and is-Group-Auto-mor-phism are both set to true.

  gap> d8 := Group( (1,2,3,4), (2,4) ); # dihedral group of order 8
  Group( (1,2,3,4), (2,4) )
  gap> a := Automorphisms( d8 );
  [ Transformation( Group( (1,2,3,4), (2,4) ), [ 1, 2, 8, 7, 5, 6, 4, 3 
       ] ), Transformation( Group( (1,2,3,4), (2,4) ), 
      [ 1, 3, 2, 7, 8, 6, 4, 5 ] ), Transformation( Group( (1,2,3,4), 
      (2,4) ), [ 1, 3, 5, 4, 8, 6, 7, 2 ] ), 
    Transformation( Group( (1,2,3,4), (2,4) ), [ 1, 5, 3, 7, 2, 6, 4, 8 
       ] ), Transformation( Group( (1,2,3,4), (2,4) ), 
      [ 1, 5, 8, 4, 2, 6, 7, 3 ] ), Transformation( Group( (1,2,3,4), 
      (2,4) ), [ 1, 8, 2, 4, 3, 6, 7, 5 ] ), 
    Transformation( Group( (1,2,3,4), (2,4) ), [ 1, 8, 5, 7, 3, 6, 4, 2 
       ] ), Transformation( Group( (1,2,3,4), (2,4) ), 
      [ 1, 2, 3, 4, 5, 6, 7, 8 ] ) ]

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