"Source: Text/Group/GrpPerm.text";
"Line: 7157";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Group/GrpPerm.text, line: 7157
// Example: H65E36 ()
print "Example: H65E36";
ei := GetEchoInput();
SetEchoInput(true);
G1 := PermutationGroup<20 |  
 [ 2, 5, 9, 11, 12, 3, 17, 13, 18, 16, 7, 15, 10, 8, 1, 
  14, 20, 19, 6, 4 ],
 [ 3, 6, 1, 10, 14, 2, 18, 17, 15, 4, 16, 13, 12, 5, 9, 
  11, 8, 7, 20, 19 ] >;
#G1;
assert $1 eq 120;
G2 := PermutationGroup<24 |
  [ 2, 4, 6, 5, 1, 7, 8, 3, 13, 15, 14, 16, 11, 9, 12, 10, 
  19, 20, 18, 17, 24, 21, 22, 23 ],
  [ 3, 1, 2, 7, 4, 9, 5, 11, 10, 6, 12, 8, 16, 15, 18, 17, 
  13, 14, 21, 23, 22, 19, 24, 20 ],
  [ 4, 5, 7, 1, 2, 8, 3, 6, 11, 12, 9, 10, 14, 13, 16, 15, 
  18, 17, 20, 19, 23, 24, 21, 22 ] >;
#G2;
assert $1 eq 120;
IsIsomorphic(G1, G2);
assert not $1;
flag, isom := IsIsomorphic(G1, Sym(5));
flag;
assert $1;
(G1.1)@ isom;
A := AutomorphismGroup(G2);
#A;
assert $1 eq 120;
#Centre(G2);
assert $1 eq 2;
OuterFPGroup(A);
A.1;
IsInnerAutomorphism(A.4);
assert not $1;
SetEchoInput(ei);
