[GAP Forum] semidirect products

[Alexander Hulpke]

Dear GAP-forum, Dear Victor Bovdi,

> Let A and B be finite 2-groups.
> I am interested in the isomorphism classes of the semidirect (or/and 
> central) products of these groups.
> 
> Do you know about a package which can aid this sort of calculation ?

There is no function that does these calculations directly -- you would have to go step-by-step in determining

- Calculate Aut(N)   (the package autpgrp will help)
- Classify all homomorphisms from G to Aut(N)   (there will be a function `AllHomomorphismClasses' in GAP4 and i can send you code for this privately if you are interested).
- Form the semidirect products using `SemidirectProduct'
- Test for isomorphism (the `anupq' package can help here, as the extensions are p-groups)

Best wishes,

   Alexander Hulpke (with help from Bettina Eick)

-- 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