[GAP Forum] Structure description of a large group

[Alexander Hulpke]

Dear Dan Langke,Dear forum,

> I have a permutation group (with two generators) of size 279936 = 2^7 * 3^7.
> How do I go about trying to find its structure description?

In general, it doesn't make much sense to try to describe the structure of an arbitrary group of that order, respectively one will end up with a description which is far from describing the isomorphism type.
The built-in `StructureDescription' function is likely to choke on a group of that size.
What one can do is for example to first find normal subgroups, see whether any of these have complements and so on.
What seems more fruitful, however, would be to use the permutation structure if the group is not too large degree. By using the action on orbits one could decompose as a subdirect product, and one could test for primitivity when acting on one orbit. If the degrees are very small one could even use `TransitiveIdentification' to identify the permutation group types.

Otherwise, it probably would make sense to think what information you really want to get from the structure description. Do you want to have a name for the group? Do you want to reconstruct the group from smaller parts? Or do you simply want to see information about its structure, the letter might be obtained easier from information such as a chief series.

Best,

Alexander Hulpke


-- Colorado State University, Department of Mathematics,
Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA
email: hulpke at math.colostate.edu, Phone: ++1-970-4914288
http://www.math.colostate.edu/~hulpke