"Source: Text/Group/GrpMatGen.text";
"Line: 3076";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Group/GrpMatGen.text, line: 3076
// Example: H66E17 ()
print "Example: H66E17";
ei := GetEchoInput();
SetEchoInput(true);
H := SU(12, 9);
// set up just unipotent classes 
U := UnipotentClasses ("SU", 12, 9);
#U;
C := ClassicalCentraliser (H, U[4][3]);
FactoredOrder (C);

K := Sp (6, 8);
// set up just semisimple classes 
S := SemisimpleClasses ("Sp", 6, 8);
// for each semisimple class rep, construct all classes for that rep 
G := Sp(6, 8);
T := [ClassesForFixedSemisimple (G, S[i][3]): i in [1..#S]];
// Total number of classes of K 
&+[#x: x in T];

// polynomial for number of classes in isometry group of this rank 
f := IsometryGroupNumberOfClasses ("SpEven", 6);
f;
Evaluate (f, 8);
SetEchoInput(ei);
