[GAP Forum] The order of Out(S4(8))
Ramon Esteban-Romero
resteban at mat.upv.es
Tue Feb 11 11:56:43 GMT 2014
Dear colleagues,
I have also found some differences between GAP versions:
┌───────┐ GAP, Version 4.7.2 of 01-Dec-2013 (free software, GPL)
│ GAP │ http://www.gap-system.org
└───────┘ Architecture: i686-pc-linux-gnu-gcc-default32
Libs used: gmp
Loading the library and packages ...
Components: trans 1.0, prim 2.1, small* 1.0, id* 1.0
Packages: AClib 1.2, Alnuth 3.0.0, AtlasRep 1.5.0, AutPGrp 1.5, CRISP
1.3.7, Cryst 4.1.12, CrystCat 1.1.6, CTblLib 1.2.2, FactInt 1.5.3, FGA
1.2.0, GAPDoc 1.5.1, IRREDSOL 1.2.3, LAGUNA 3.6.4, Polenta 1.3.1,
Polycyclic 2.11, RadiRoot 2.6, ResClasses 3.3.2,
Sophus 1.23, SpinSym 1.5, TomLib 1.2.4
Try '?help' for help. See also '?copyright' and '?authors'
gap> S:=PSp(4,8);
<permutation group of size 1056706560 with 2 generators>
gap> A:=AutomorphismGroup(S);
<group with 4 generators>
gap> Size(A)/Size(S);
3
┌───────┐ GAP, Version 4.6.5 of 20-Jul-2013 (free software, GPL)
│ GAP │ http://www.gap-system.org
└───────┘ Architecture: i686-pc-linux-gnu-gcc-default32
Libs used: gmp
Loading the library and packages ...
Components: trans 1.0, prim 2.1, small* 1.0, id* 1.0
Packages: AClib 1.2, Alnuth 3.0.0, AutPGrp 1.5, CRISP 1.3.7, Cryst
4.1.11, CrystCat 1.1.6, CTblLib 1.2.2, FactInt 1.5.3, FGA 1.2.0, GAPDoc
1.5.1, IO 4.2, IRREDSOL 1.2.3, LAGUNA 3.6.3, Polenta 1.3.1, Polycyclic
2.11, RadiRoot 2.6, ResClasses 3.3.0, Sophus 1.23,
SpinSym 1.5, TomLib 1.2.2
Try '?help' for help. See also '?copyright' and '?authors'
gap> S:=PSp(4,8);
<permutation group of size 1056706560 with 2 generators>
gap> A:=AutomorphismGroup(S);
<group with 8 generators>
gap> Size(A)/Size(S);
6
Best wishes,
--
Ramon <Ramon.Esteban at uv.es>
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Al 11/02/14 12:09, En/na Anvita ha escrit:> Dear Dmitrii,
>
> Here is a more detailed output which includes GAP version and
architecture.
>
> ┌───────┐ GAP, Version 4.7.2 of 01-Dec-2013 (free software, GPL)
> │ GAP │ http://www.gap-system.org
> └───────┘ Architecture: x86_64-unknown-linux-gnu-gcc-default64
> Libs used: gmp, readline
> Loading the library and packages ...
> Components: trans 1.0, prim 2.1, small* 1.0, id* 1.0
> Packages: AClib 1.2, Alnuth 3.0.0, AtlasRep 1.5.0, AutPGrp 1.5,
> Browse 1.8.3, CRISP 1.3.7, Cryst 4.1.12, CrystCat 1.1.6,
> CTblLib 1.2.2, FactInt 1.5.3, FGA 1.2.0, GAPDoc 1.5.1, IO
4.2,
> IRREDSOL 1.2.3, LAGUNA 3.6.4, Polenta 1.3.1, Polycyclic 2.11,
> RadiRoot 2.6, ResClasses 3.3.2, Sophus 1.23, SpinSym 1.5,
> TomLib 1.2.4
> Try '?help' for help. See also '?copyright' and '?authors'
> gap> S:=PSp(4,8);
> <permutation group of size 1056706560 with 2 generators>
> gap> A:=AutomorphismGroup(S);
> <group with 4 generators>
> gap> Size(A)/Size(S);
> 3
> gap>
>
> Please, note that the number of generators of Aut(S) differs from that in
> your calculation, too.
>
> Anvita
>
>
> On Tue, Feb 11, 2014 at 5:32 PM, Dmitrii Pasechnik <
> dmitrii.pasechnik at cs.ox.ac.uk> wrote:
>
>> Dear Forum,
>> it works for me (on OSX 10.6.8):
>>
>> ********* GAP, Version 4.6.4 of 04-May-2013 (free software, GPL)
>> * GAP * http://www.gap-system.org
>> ********* Architecture: x86_64-apple-darwin10.8.0-gcc-default64
>> Libs used: gmp, readline
>> Loading the library and packages ...
>> Packages: Alnuth 3.0.0, AutPGrp 1.5, CTblLib 1.2.2, FactInt 1.5.3,
>> GAPDoc 1.5.1, LAGUNA 3.6.3, Polycyclic 2.11
>> Try '?help' for help. See also '?copyright' and '?authors'
>> gap> S:=PSp(4,8);
>> <permutation group of size 1056706560 with 2 generators>
>> gap> OrbitLength(S,1);
>> 585
>> gap> NormalSubgroups(S);
>> [ Group(()), <permutation group of size 1056706560 with 2 generators> ]
>> gap> A:=AutomorphismGroup(S);
>> <group with 8 generators>
>> gap> Order(A)/Order(S);
>> 6
>> gap> Size(A)/Size(S);
>> 6
>>
>>
>> What version of GAP are you using, and on which OS/hardware?
>>
>> On Tue, Feb 11, 2014 at 01:08:22PM +0700, Anvita wrote:
>>> Dear Forum,
>>>
>>> According to the ATLAS, the simple group S4(8) has outer automorphism
>> group
>>> of order 6,
>>> but the following calculation, if I am interpreting it correctly, seems
>> to
>>> suggest that it has order 3.
>>>
>>> Anvita
>>>
>>>
>>> gap> S:=PSp(4,8);
>>> <permutation group of size 1056706560 with 2 generators>
>>> gap> A:=AutomorphismGroup(S);
>>> <group with 4 generators>
>>> gap> Size(A)/Size(S);
>>> 3
>>> _______________________________________________
>>
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