I am not sure if this helps you, but maybe check out StructureDescription:
https://www.gap-system.org/Manuals/doc/ref/chap39.html#X87BF1B887C91CA2E
Best,
Gabor
On Sun, 17 Dec 2017, Martin Rubey wrote:
Dear Josh, Dear Forum,
Joshua Hunt <joshuah...@math.ku.dk> writes:
I'm afraid I don't quite understand your objection to the SmallGroup
library. What requirements does it not fulfil?
Essentially: it doesn't cover S_7, S_5 ยง Z_2, etc.
So: the small group ID is just perfect for the "small" objects, but it
simply doesn't work for enough groups obtained as images of maps from,
say, graphs to groups.
In fact, that's what you write here:
I would also point out that "groups of order less than 47" doesn't
cover a lot of groups you probably would care about
(e.g. symmetric/alternating groups S_5/A_5 and bigger, as mentioned
in your example).
Let me try to put it in different words:
when initialising the findstat database,
* first we compute the canonical forms of the small objects (for groups:
order less than 47)
* then we apply the maps in the database (eg, "automorphism group of a
graph", "Weyl group of a finite Cartan type", "center of a group"),
and compositions of two and three maps, to all small objects (eg,
graphs, finite Cartan types, groups,...), and compute canonical forms
of those.
Does this make it clearer?
Best,
Martin
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