Are there any?
In any case, first load the GAP database with
sage -i database_gap-4.4.9
Then you might try something like this:
for n in range(4,200):
gap.eval("ngs := NumberSmallGroups( %s );;"%n);
m = int(gap("ngs")) ## number of gps of size n
for j in range(1,m+1):
gap.eval("G := SmallGroup( %s, %s );;"%(n,j));
gap.eval("irr:=Irr(G);;"); ## = list of irr chars of G
N = int(gap.eval("Length(irr)")) ## = number of irrs of G
degs = [int(gap.eval("irr[%s][1]"%k)) for k in range(1,N+1)]
print n,m,j,N,degs
if set(degs)==set([1,2,5]): ## checks your condition
print degs
print gap.eval("G"), "\n"
Comments:
(1) it picks up lots of
ERROR: Magic function `print` not found.
statements. I don't know what these mean or how serious they are.
(2) This is not very SAGE-native since GAP decides whether to output
SmallGroups as either a permutation group or a PC ("polycyclic") group.
When or why it does which, I'm not sure. (Before wrapping PC groups in
SAGE, I was hoping for Jack Schmidt's help and also further information
about how the polycyclic GAP package is licensed....)
(3) One could do this using almost entirely permutation groups, but it
would be slower and a bit more painful. Hope this helps as it is.
On 4/27/07, Andrew <[EMAIL PROTECTED]> wrote:
>
> Hello,
>
> I had heard that it was possible, in Sage, to link into the small
> groups
> database of groups of order < 2000 (more or less). I was wondering,
> particularly:
>
> 1) Is it possible to say, loop through groups of order < 200?
>
> 2) Is it possible in Sage to take a group G and produce its character
> table?
>
> 3) If the answers to questions 1 and 2 are yes, approximately what
> would code
> look like to print out all groups of order < 200 whose representations
> are of
> degrees 1, 2, and 5 only (and including all three of these degrees, so
> not, for
> example, abelian and dihedral groups)?
>
> Thanks,
>
> Andrew Dittmer
>
>
> >
>
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