"Source: Text/Group/GrpPC.text";
"Line: 5482";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Group/GrpPC.text, line: 5482
// Example: H70E34 ()
print "Example: H70E34";
ei := GetEchoInput();
SetEchoInput(true);
G := SmallGroup(576, 4123);
G;
SL := Subgroups(G);
T := {X`subgroup: X in SL};
#T;
assert $1 eq 243;
TrivCore := {H:H in T| #Core(G,H) eq 1};
mdeg := Min({Index(G,H):H in TrivCore});
Good := {H: H in TrivCore| Index(G,H) eq mdeg};
#Good;
assert $1 eq 3;
H := Rep(Good);
f,P,K := CosetAction(G,H);
#K;
assert $1 eq 1;
IsPrimitive(P);
assert not $1;
SetEchoInput(ei);
