"Source: Text/Group/GrpPerm.text";
"Line: 2881";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Group/GrpPerm.text, line: 2881
// Example: H65E17 ()
print "Example: H65E17";
ei := GetEchoInput();
SetEchoInput(true);
M := PermutationGroup< 30 |
        (1,2,3)(4,14,8)(5,15,9)(6,13,7)(25,27,26),
        (4,20,13)(5,21,14)(6,19,15)(16,17,18)(27,28,29),
        (1, 15)(2, 13)(3, 14)(4, 22)(5, 23)(6, 24)(7, 18)(8, 16)
          (9, 17)(10, 21)(11, 19)(12, 20)(25, 29)(26, 27)(28, 30) >;
FactoredOrder(M);
S2 := SylowSubgroup(M, 2);
S2;
b := exists(t){ x : x in M | Order(S2 meet S2^x) eq 1 };
b;
assert $1;
S2a := S2^t;
N := Normalizer(M, S2);
N;
SetEchoInput(ei);
