gap> f:=FreeGroup("a","b");
<free group on the generators [ a, b ]>
gap> g:=f/[f.1^5, f.2^2, f.2*f.1*f.2^-1*f.1];
<fp group on the generators [ a, b ]>
gap> List(g);
[ id, b, a^4*b, a, a^4, a*b, a^3*b, a^2, a^3, a^2*b ]

gap> a:=AutomorphismGroup(g);
<group of size 20 with 3 generators>
gap> List(a);
[ IdentityMapping( <fp group of size 10 on the generators [ a, b ]> ), [ b, a ] -> Pcgs([ a*b, a ]),
  [ a, b*a^2 ] -> [ a, b ], [ a, a^2*b ] -> [ a, b ], [ a, a*b ] -> [ a, b ], [ a^-1, b ] -> [ a, b ],
  [ a^-1, a*b ] -> [ a, b ], [ a*b, a^-1 ] -> Pcgs([ a*b, a ]), [ a^-1, b*a^2 ] -> [ a, b ],
  [ a^-1, b*a ] -> [ a, b ], [ a^2, b ] -> [ a, b ], [ a^2, b*a^2 ] -> [ a, b ], [ a^2, a*b ] -> [ a, b ],
  [ a*b, a^2 ] -> Pcgs([ a*b, a ]), [ a^2, a^2*b ] -> [ a, b ], [ a^-2, b ] -> [ a, b ], [ a^-2, a^2*b ] -> [ a, b ],
  [ a^-2, b*a ] -> [ a, b ], [ a^-2, a*b ] -> [ a, b ], [ a^-2, b*a^2 ] -> [ a, b ] ]