Dear Pubbers It is well known that Out(J2) =2. I found permutation representation of this group in the website of "Atlas of Finite Group Representations". In GAP, these permutations generate the group J2, but Aut(J2) is again isomorphic to J2. What is happened?
In gap4r6 we have: gap> b11 := (1,84)(2,20)(3,48)(4,56)(5,82)(6,67)(7,55)(8,41)(9,35)(10,40)(11,78)(12, > 100)(13,49)(14,37)(15,94)(16,76)(17,19)(18,44)(21,34)(22,85)(23,92)(24, > 57)(25,75)(26,28)(27,64)(29,90)(30,97)(31,38)(32,68)(33,69)(36,53)(39,61) > (42,73)(43,91)(45,86)(46,81)(47,89)(50,93)(51,96)(52,72)(54,74)(58,99) > (59,95)(60,63)(62,83)(65,70)(66,88)(71,87)(77,98)(79,80);; gap> b21 := (1,80,22)(2,9,11)(3,53,87)(4,23,78)(5,51,18)(6,37,24)(8,27,60)(10,62,47) > (12,65,31)(13,64,19)(14,61,52)(15,98,25)(16,73,32)(17,39,33)(20,97,58) > (21,96,67)(26,93,99)(28,57,35)(29,71,55)(30,69,45)(34,86,82)(38,59,94) > (40,43,91)(42,68,44)(46,85,89)(48,76,90)(49,92,77)(50,66,88)(54,95,56) > (63,74,72)(70,81,75)(79,100,83);; gap> g:=Group(b11,b21);; gap> h:=AutomorphismGroup(g);; gap> Size(g); 604800 gap> Size(h); 1209600 gap> Size(h)/2; 604800 But in gap4r7 we obtain that Size(g)=Size(h). This shows that probably gap4r7 has a bug. Am I right? Best regards Fatemeh -- Regards; Miss Fatemeh Koorepazan-Moftakhar PhD Candidate, Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Iran _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
