[GAP Forum] Constructing semilinear, outer linear, and affine groups

[Vipul Naik]

Dear GAP Forum,

I would appreciate if any of you could provide me code (or suggest a
package) that would help construct these groups for a positive integer
n and a prime power q of prime p. If I have the code, I should be able
to tweak it to construct the variants. I am not too concerned about
computational efficiency:

(1) General semilinear group Gamma L(n,q), defined as semidirect
product with base GL(n,q) and acting group the automorphism group of
F_q (i.e., the Galois group of F_q over F_p).

I'm also interested in constructing variants where the base group is
taken as SL(n,q), PGL(n,q), or PSL(n,q), and also variants where we
take a subgroup of the Galois group rather than the whole Galois group.

(2) Outer linear group OL(n,q), defined as the semidirect product of
GL(n,q) by a cyclic group of order two where the non-identity element
acts by the transpose-inverse map.

I also want to consider variants where the base group is taken as
SL(n,q) instead of GL(n,q), as well as the variant where q = p^2 and
we take the semidirect product by a cyclic group of order two acting
by the conjugate-transpose-inverse.

(3) General affine group denoted GA(n,q) or AGL(n,q) defined as the
semidirect product of the n-dimensional vector space over F_q by
GL(n,q) with its natural action.

I also want to construct semidirect products for chosen subgroups of
GL(n,q), and more generally, semidirect products associated with
n-dimensional representations of groups over F_q.

Thank you!

Vipul