# 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 ] ) ]
```

GAP 3.4.4
April 1997