/*
Words to get from G1-standard generators of J4, (a,b), to the
presentation (G2) generators, (x,y,t).
Have <x,y> = M24. <x,z> = 2^6:(S3 x L3(2)) commutes with involution t.
*/

x:=((a*b*a*b^2)^5)^((a*b)^4);
y:=((a*b^2)^4)^((a*b)^2*(b*a)^18);
z:=(x*y)^2*(x*y^2)^2*(x*y)^3;
c:=a^(a*b*a*b^3*(a*b*a*b^2)^3);
t:=(c*z)^15;