big-hard

# ACEExample "big-hard" : enumeration of cosets of H in G,
# where |G| = 2^18.3, |G : H| = 6, using hard strategy.
#
local F, G, a, b, c, x, y, A, B, C;
# We define a group G of order 2^18.3 on 5 generators
F := FreeGroup("a","b","c","x","y"); 
     a := F.1;  b := F.2;  c := F.3;  x := F.4; y := F.5;
     A := a^-1; B := b^-1; C := c^-1;
G := F / [a*B*C*b*a*c, b*A*C*b*a*a*c*A, a*c*c*A*A*B*a*b,
          x^2, Comm(a,x), Comm(b,x), Comm(c,x),
          y^3, Comm(a,y), Comm(b,y), Comm(c,y), Comm(x,y)];
return ACEfunc(
    FreeGeneratorsOfFpGroup(G), 
    RelatorsOfFpGroup(G), 
    [a*B*C*b*a*c, b*A*C*b*a*a*c*A, a*c*c*A*A*B*a*b] # |G : H| = 6
    # Options that don't affect the enumeration
    : echo, enum := "G (order 2^18.3)", subg := "H (index 6)", 
    # Other options
    hard, mend, ct := 2000, no := 11, pmod := 2, fill := 2, 
    dsiz := 15000, mess := 100000, wo := "2500k");