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FindPos := function(list, x)
local n, i;
n := Length(list);
for i in [1..n] do
if x in list[i] then
return i;
fi;
od;
end;
id := function(x)
return x;
end;
Subgroupladder := function(G)
local
orb,
i,
k,
n,
pair,
ladder,
directfactors,
mapping,
output,
partition;
if (not IsPermGroup(G)) then
ErrorNoReturn("the argument must be a permutation group!\n");
fi;
n := LargestMovedPoint(G);
orb := List(Orbits(G), x -> x);
SortBy(orb, x->-Length(x));
output := [];
partition := List(orb, Length);
mapping := List([1..n], x -> FindPos(orb, x));
ladder := [[List(partition, id), List(mapping, id)]];
while (Length(partition) <> 1 or partition[1] < n) do
if (Length(partition) = 1 and partition[1] < n) then
mapping[Position(mapping, 0)] := 1;
partition[1] := partition[1] + 1;
Add(ladder, [List(partition, id), List(mapping, id)]);
else
if (partition[2] = 1) then
Remove(partition, 2);
for i in [1..n] do
if (mapping[i]) > 1 then
mapping[i] := mapping[i] - 1;
fi;
od;
partition[1] := partition[1] + 1;
Add(ladder, [List(partition, id), List(mapping, id)]);
else
mapping[Position(mapping, 2)] := Length(partition)+1;
partition[2] := partition[2] - 1;
Add(partition, 1);
Add(ladder, [List(partition, id), List(mapping, id)]);
mapping[Position(mapping, Length(partition))] := 1;
Remove(partition);
partition[1] := partition[1] + 1;
Add(ladder, [List(partition, id), List(mapping, id)]);
fi;
fi;
od;
for pair in ladder do
k := Length(pair[1]);
mapping := pair[2];
directfactors := [];
for i in [1..k] do
Add(directfactors, SymmetricGroup(Filtered([1..n], x -> i = mapping[x])));
od;
Add(output, DirectProduct(directfactors));
od;
return output;
end;
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