[GAP Forum] Conway Co2 group

[Rudolf Zlabinger]

I try to handle the Conway Co2 group in GAP. I formed a Fpgroup with the relators as given in the ATLAS as follows:

gap> START_TEST("The Conway Group Co2.txt");
gap> fgco2:=FreeGroup("a","b","c","d","e","f","g");;
gap> a:=fgco2.1;;   
gap> b:=fgco2.2;;
gap> c:=fgco2.3;;
gap> d:=fgco2.4;;
gap> e:=fgco2.5;;
gap> f:=fgco2.6;;
gap> g:=fgco2.7;;
gap> relators:=[a/(c*f)^2,b/(e*f)^3,e/(b*g)^2,(a*e*c*d)^4,(c*e*f)^7,(b*a*e*f*g)^3];;
gap> Append(relators,[a^2,b^2,c^2,d^2,e^2,f^2,g^2]);;
gap> Append(relators,[(a*b)^3,(a*c)^2,(a*d)^2,(a*e)^4,(a*f)^2,(a*g)^2]);;
gap> Append(relators,[(b*a)^3,(b*c)^5,(b*d)^2,(b*e)^2,(b*f)^2,(b*g)^4]);;
gap> Append(relators,[(c*b)^5,(c*d)^3,(c*e)^3,(c*f)^4,(c*g)^2]);;
gap> Append(relators,[(d*c)^3,(d*e)^2,(d*f)^3,(d*g)^2]);;
gap> Append(relators,[(e*a)^4,(e*c)^3,(e*f)^6,(e*g)^2]);;
gap> Append(relators,[(f*c)^4,(f*d)^3,(f*e)^6,(f*g)^4]);;
gap> Append(relators,[(g*b)^4,(g*f)^4]);;
gap> co2:=fgco2/relators;;
gap> STOP_TEST( "The Conway Group Co2",1000);

The size of the group is 2^18*3^6*5^3*7*11*23 = 42305421312000;

The standard operations as IsFinite, ConjugacyClasses, Size and others, run out of time > 1 hour on my small machine of 500 Mhz, 128MB. 

Is there, as you know,  any chance to handle this Fpgroup smoothly on a machine of 3,5Ghz, 500MB ( I mean times <= 15 minutes)? I currently try to find a representation in a permutation group, would that help?

Thank you for hints, Rudolf Zlabinger