[GAP Forum] The order of Out(S4(8))

[Anvita]

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
> > _______________________________________________
>