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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it

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# U/<yu,v> from Edeson's thesis (p. 46)

Gr: y,u,v;
Rel: y^2, (yu)^2, u^3, (yv)^2, v^3, (uv)^6, (uV)^6, (yuv)^6, (y(uv)^3)^6;
Gen: yu,v;

Mess:10000;

Sims:3;  End;			# m=86 t=101

Sims:9;  End;			# m=40 t=43

Fel:1;  End;			# m=78 t=80
No:7;   End;			# m=36 t=37

# Duplicate table at top of p.48

AsIs:1;
Gr:u,v,y;
Rel: y^2, (yu)^2, u^3, (yv)^2, v^3, (uv)^6, (uV)^6, (yuv)^6, (y(uv)^3)^6;
Gen: yY, uU, yu, v;

Fel;
Loop:1;  Begin;
Loop:2;  Redo;
Pr:-3;

# Use Aep with this to give `best' enumeration ...