A5-C5

# ACEExample "A5-C5" : enumeration of cosets of H in G,
# where G = A_5, H = C_5,  using default strategy.
#
local F, a, b, G;
F := FreeGroup("a","b"); a := F.1;  b := F.2;
G := F / [a^2, b^3, (a*b)^5 ];
return ACEfunc(
    # Arguments
    FreeGeneratorsOfFpGroup(G), RelatorsOfFpGroup(G), [a*b]
    # Options
    : echo, # Echo handled by GAP (not ACE)
      enum := "A_5",  # Give the group G a meaningful name
      subg := "C_5"); # Give the subgroup a meaningful name