Dear GAP-Forum

At 03:10 PM 6/16/99 +0100, Olivier Cormier wrote:
>
>how to compute the semidirect product of G by H where G and H are any 2
>groups, without knowing the action of G on H?
>(My aim is to compute it when G is the extraspecial group of order 5^3
>and exponent 5 and H is SL(2,5)).

In general, there is no such thing as "the semidirect product".
Any of the possible product corresponds to a particular action of
H on G.

Do you mean something like "a semidefinite product that
corresponds to the natural action of SL_2(5) on G/Z(G) ?"

You can construct such a group as a subgroup of
GL_4(5), as follows.

G= <
1 w 0 0
0 1 0 w^-1
0 0 1 0
0 0 0 1  and

1 0 1 0
0 1 0 1
0 0 1 0
0 1 0 1 >
(where w is a primitive element of GF(5))

and H = <
1000
0110
0010
0001 and

1000
0100
0110
0001
>

Hope this helps,
Dmitrii

Dmitrii Pasechnik
Dept. of Computer Science
Utrecht University
PO Box 80089
3508 TB Utrecht
The Netherlands

e-mail: dima@cs.uu.nl
http://www.cs.uu.nl/staff/dima.html