Dear Forum,

I wrote:

I have a large group, a quotient of an infinite group on five
generators. I have a permutation representation of it on 50 points,
and would like to find a presentation for it.

Thanks to all those who replied.

One person asked why I wanted the presentation when I already
had an permutation representation. The reason is that the group is
the group of a regular polytope, and the permutation representation
gives little intuitive understanding of the structure of the polytope.
The presentation will give that understanding.

Two people suggested that my group might be easier to handle in
GAP 4.3, and asked that I give them the permutation presentation.
Actually, I have two groups, one of size 943718400, and one only
half as big.

The larger one is 
Group( [ (15,21)(18,25)(22,28)(26,31)(29,34),
 ( 4, 6)( 7, 9)(10,12)(11,15)(13,18)(14,17)(16,22)(19,26)(20,24)(21,27)
(23,29)(25,30)(28,33)(31,36)(34,39)(35,38)(40,43)(41,44)(45,48)
(46,49),
( 3, 4)( 5, 7)( 8,11)(10,13)(12,16)(14,19)(17,23)(18,22)(20,24)(25,28)
(26,29)(27,32)(30,35)(31,34)(33,38)(36,41)(37,40)(39,44)(42,45)
(46,49),
( 2, 3)( 5, 8)( 7,10)( 9,12)(11,13)(14,20)(15,18)(17,24)(19,23)(21,25)
(26,29)(27,30)(31,34)(32,37)(35,40)(36,39)(38,43)(41,46)(42,47)
(44,49),
( 1, 2)( 3, 5)( 4, 7)( 6, 9)(10,14)(12,17)(13,19)(16,23)(18,26)(22,29)
(25,31)(28,34)(30,36)(33,39)(35,41)(37,42)(38,44)(40,45)(43,48)
(47,50) ] )

One person suggested I try to find the FP group using
IsomorphismFpGroupByCompositionSeries

I will. Hopefully it will be faster that my current attempt,
and give a suitable answer.

Thanks once again!

Michael Hartley : Michael.Hartley@sit.edu.my
Head, Department of Information Technology,
Sepang Institute of Technology
+---Q-u-o-t-a-b-l-e---Q-u-o-t-e----------------------------------
"There was a young man from Peru,
Whose limericks stopped at line two."
-- Spike Milligan