Hi gap forum, can anyone explain the following behavior to me (saying that PSL(3,2) has to distinct conjugacy classes that are conjugate)?
vec1:=[1,0,0]*Z(2)^0;; sl:=SL(3,2);; orb:=Orbit(sl,vec1,OnLines);; act:=ActionHomomorphism(sl,orb,OnLines);; psl:=Image(act);; ConjugacyClasses(psl); [ ()^G, (3,4)(6,7)^G, (2,3,5,4)(6,7)^G, (2,3,6)(4,7,5)^G, (1,2,3,4,7,5,6)^G, (1,2,3,5,6,7,4)^G ] g:=Representative(ConjugacyClasses(psl)[5]);; h:=Representative(ConjugacyClasses(psl)[6]);; c:=(2,6,4)(3,5,7);; c*g^(-1)*c^(-1)=h; true IsSubgroup(psl,Group(c)); true I guess one could as well use PSL(3,2) out of the box but that gives a different permutation presentation and I didn't want to work out c anew. I also know that PSL(3,2)=SL(3,2)=GL(3,2) etc., but that's not the point of the question. (I do not know what would be the right way to say "IsElement(psl,c)" in the end, so I would be interested in that.) Thanks for the help! Best regards, Stefan P.S.: In case you are wondering, I'm using GAP version 4.4.12. _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
