Involutions in the Automorphism Groups of Small Sporadic Simple Groups

Algorithm 1

F<a,b>:=FreeGroup(2);

phi:=hom< F->G  ∣  <a,G.1>,<b,G.2> >;

r,h:=IsConjugate(G,t,x);

sh:=h@@phi;

lengthmin:=#sh;

hmin:=h;

Ct:=Centralizer(G,t);

for c in Ct do

  sch:=(c*h)@@phi;

   if #sch lt lengthmin then

    lengthmin:=#(sch);

    hmin:=c*h; shmin:=sch;

  end if;

end for;