"Source: Text/Group/GrpPerm.text";
"Line: 4975";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Group/GrpPerm.text, line: 4975
// Example: H65E28 ()
print "Example: H65E28";
ei := GetEchoInput();
SetEchoInput(true);
G := sub< Sym(100) |
  (1,21,41,61,81)(2,82,62,42,22)(3,23,43,63,83)(4,84,64,44,24)
    (5,25,45,65,85)(6,86,66,46,26)(7,27,47,67,87)(8,88,68,48,28)
    (9,29,49,69,89)(10,90,70,50,30)(11,31,51,71,91)(12,92,72,52,32)
    (13,33,53,73,93)(14,94,74,54,34)(15,35,55,75,95)(16,96,76,56,36)
    (17,37,57,77,97)(18,98,78,58,38)(19,39,59,79,99)(20,100,80,60,40),
  (1,4,6,7,10)(2,3,5,8,9)(11,19,17,15,14)(12,20,18,16,13)(21,24,26,27,30)
     (22,23,25,28,29)(31,39,37,35,34)(32,40,38,36,33)(41,44,46,47,50)
     (42,43,45,48,49)(51,59,57,55,54)(52,60,58,56,53)(61,64,66,67,70)
     (62,63,65,68,69)(71,79,77,75,74)(72,80,78,76,73)(81,84,86,87,90)
     (82,83,85,88,89)(91,99,97,95,94)(92,100,98,96,93),
  (1,11,2,12)(3,13,4,14)(5,16,6,15)(7,17,8,18)(9,20,10,19)(21,31,22,32)
     (23,33,24,34)(25,36,26,35)(27,37,28,38)(29,40,30,39)(41,51,42,52)
     (43,53,44,54)(45,56,46,55)(47,57,48,58)(49,60,50,59)(61,71,62,72)
     (63,73,64,74)(65,76,66,75)(67,77,68,78)(69,80,70,79)(81,91,82,92)
     (83,93,84,94)(85,96,86,95)(87,97,88,98)(89,100,90,99) >;
MaxPart := MaximalPartition(G);
#MaxPart;
assert $1 eq 2;
MaxPart;
MinPart := MinimalPartition(G);
#MinPart;
assert $1 eq 50;
Parts := MinimalPartitions(G);
[ #p : p in Parts ];
f, Im, Ker := BlocksAction(G, Parts[1]);
f;
Im;
Ker;
SetEchoInput(ei);
