> < ^ Date: Wed, 25 Nov 1998 18:25:03 +0000 (GMT)
> < ^ From: Alexander Hulpke <hulpke@math.colostate.edu >
^ Subject: Re: Subgroup lattice (was: help)

Dear GAP Forum,

I am working with GAP 3.4.4 version for mac PPC. The groups that I am
investigating are transitives, imprimitives and are contained in S_12.
However now the size of some of this groups gives to me problems. For

example:

```gap> g:=Group((1,2)(3,4),(1,3,5)(2,4,6),(3,5,7,9,11)(4,6,8,10,12));
Group( (1,2)(3,4), (1,3,5)(2,4,6), ( 3, 5, 7, 9,11)( 4, 6, 8,10,12) )
gap> Size(g);
11520
gap> lat:=Lattice(g);
Error, sorry, can' t identify the group's solvable residuum in
```

You have reached the limits of the capabilities of GAP 3 as documented in
the manual.
The subgroup lattice program in GAP 3 is only guaranteed to work if the
groups solvable residuum is not larger than 5000. (The algorithm uses a data
base of recomputed information and this information is not available for
larger groups). Your group <g> is perfect an thus equal to its solvable
residuum, so there is no easy way to compute the subgroup lattice.
The only way around this problem would be to provide the pwerfect subgroups
a priori from theory.
The manual secion on `Lattice' gives an example on how to do this.

The subgroup lattice function in GAP 4 has been improved and will work for
much larger groups (and -- provided memory being available -- should work
for all subgroups of S12).
However the code is quite different and thus it is not possible to make this
available for GAP 3.

If I have the generators of the group ? how to request to GAP subgroups
of certain size.

Unless the subgroups are of prime power order the only general algorithm I
am aware of would be to use the subgroup lattice, so there is no way around
this problem in GAP 3.

Best regards,

Alexander Hulpke

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