"Source: Text/Group/GrpAuto.text";
"Line: 815";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Group/GrpAuto.text, line: 815
// Example: H74E7 ()
print "Example: H74E7";
ei := GetEchoInput();
SetEchoInput(true);
G := SmallGroup(904, 4);
FactoredOrder(G);
FactoredOrder(Centre(G));
A := AutomorphismGroup(G);
FactoredOrder(A);
HasAttribute(A, "FpGroup");     
assert not $1;
HasAttribute(A, "OuterFpGroup");
assert not $1;
F,m := FPGroup(A);
AssertAttribute(A, "FpGroup", <F,m>);
n := NormalSubgroups(G);
[x`order : x in n];
characteristics := [s : x in n |
  forall{f: f in Generators(A) | s@f eq s}
  where s is x`subgroup]; 
[#s : s in characteristics];
SetEchoInput(ei);
