[GAP Forum] StructureDescription Revisited

[Nilo de Roock]

Hello GAP forum,

I have posted some questions regarding StructureDescription()
recently, thank you for all answers. ( It came a bit as a shock to me
but I now understand that non-isomorphic groups can have the same
structure description. So yes the answers have been -very- helpful. I
have also updated to the latest GAP releases, both kernel and
packages. )

I am however still a bit uncertain about how I should interpret the
answers of StructureDescription() and what is the best (simplest)
method of finding the structure of a group. Let me give an example.

<EXAMPLE>
I am doing some experiments regarding generating sets of matrices and
the structure of the group they generate. I use for example the
following function:

testG:=function(a,b)
	local M1;
	M1:=[[ [ 0, -E(a)^-1 ], [ -E(a), 0 ] ],[ [ 0, -1 ], [ 1, 0 ] ], [ [
E(4*b), 0 ], [ 0, -E(4*b) ] ],[ [ -1, 0 ], [ 0, -1 ] ]];
	return (Group(M1));
end;

I noticed the (for me...) interesting result that
StructureDescription(testG(8,1)) = QD16
StructureDescription(testG(8,3)) =C3 X QD16
StructureDescription(testG(8,5))= C5 X QD16
For other numbers however...
StructureDescription(testG(8,2))= GAP Error*
StructureDescription(testG(8,4))= GAP Error*
StructureDescription(testG(8,7))=  GAP Error*

*="... Error, no method found! For debugging hints type ?Recovery from
NoMethodFound
Error, no 2nd choice method found for `IsNaturalGL' on 1 arguments called fro\
m..."
( I interpreted the errors as "does not generate a group", or a bug in
StructureDescription() for which a fix is due...)

Size(testG(8,1))= 16
Size(testG(8,2))= 64
Size(testG(8,3))= 48
Size(testG(8,4))= 128
Size(testG(8,5))= 80
Size(testG(8,6))= 192
Size(testG(8,7))= 112
So there -are- groups generated. But which ones?

( Starting from Size(testG(4,7*11))= 176 computation time increased noticably. )
</EXAMPLE>

In this particular example I would very much like to know which group
is generated in testG(8,2). Can GAP give an answer to that? Will the
forthcoming update in StructureDescription() address this issue(if an
issue at all)?

More in general, am I perhaps using StructureDescription() in a wrong
way or am I expecting too much from the command?

Thanks in advance for any advice.
nilo