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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

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