[GAP Forum] Report of a bug in gap4r7

[Alexander Hulpke]

Dear Forum, Dear Ms. Mofatkhar,

> 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?

This is a misprint in a stored list of automorphism group orders: The list for sporadic groups with automorphism group of order 2 lists “HJ” instead of the consistent  “J2” (as which the group is recognized) and thus the automorphism group routine does not realize there is an automorphism to be looked for. This will be fixed in the next release.

Thank you for reporting the error,

   Alexander Hulpke


> 
> 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
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