[GAP Forum] Working with large conjugacy class

[Marek Mitros]

Hi,

I perform following code in GAP 4.5.5- see below. I see that single
matrix 133x133 over GF(4) use 8902 bytes of memory. The size of 2A
class is 1 539 000. So (1 539 000 * 8902)/2^20 = 13 065 MB.

I start gap session with option -o 15000m (is it OK to allocate 15 GB
of memory ?). And I run command
c2s:= AsList(c2);;

Is there hope to fit whole conjugacy class in memory ? Are there other
ways to loop through all large conjugacy class without storing it in
memory ? I could store it on the disk for example.

I would like to get answer on following questions and other similar.
Fix v0 in 2A conjugacy class. I call element x "perpendicular to v0"
if Order(x*v0)=2. How many elements there are perpendicular to v0 ?
What is the size of maximal commuting subset in 2A. What is the size
of abelian group generated by it ? What is the size of set {x: x*v0
belongs to 2A} ?

Thanks for any advice.
Regards,
Marek


gap> hn:=AtlasGroup("HN", Dimension, 133);
<matrix group of size 273030912000000 with 2 generators>
gap> gens:=GeneratorsOfGroup(hn);
[ < immutable compressed matrix 133x133 over GF(4) >, < immutable
compressed matrix 133x133 over GF(4) > ]
gap> Order(gens[1]);
2
gap> c2:=ConjugacyClass(hn,gens[1]);
< immutable compressed matrix 133x133 over GF(4) >^G
gap> MemoryUsage(gens[1]);
8902