//load "/home/michler/PermutationConstituents.mag";
//load "D:/magmadoc/PermutationConstituents.mag";
//SetLibraryRoot("/home/michler/Magma2r11p8/libs/");

G:=ATLASGroup("J1");
prk:=PermRepKeys(G);
str:="";
for p in [1..5] do 
    grp:=PermutationGroup(prk[p]);   
    subg:=Stabilizer(grp,1);
    ChiefFactors(subg);
    time mat:=PermutationConstituents(grp,subg);
    tmp:="J_1&" cat Sprint(#subg) cat "&" cat Sprint(Degree(grp)) 
    cat "&" cat Sprint(#mat) cat "&" cat "\\\\\\hline" cat "\n";
    str cat:=tmp;
end for;

G:=ATLASGroup("HS");
prk:=PermRepKeys(G);
str:="";
for p in [1..6] do  
    grp:=PermutationGroup(prk[p]);   
    subg:=Stabilizer(grp,1);
    ChiefFactors(subg);
    time mat:=PermutationConstituents(grp,subg);
    tmp:="J_1&" cat Sprint(#subg) cat "&" cat Sprint(Degree(grp)) 
    cat "&" cat Sprint(#mat) cat "&" cat "\\\\\\hline" cat "\n";
    str cat:=tmp;
end for;

nam:="J2";
G:=ATLASGroup(nam);
prk:=PermRepKeys(G);
str:="";
for p in [1..#prk] do  
    grp:=PermutationGroup(prk[p]);   
    subg:=Stabilizer(grp,1);
    ChiefFactors(subg);
    time mat:=PermutationConstituents(grp,subg);
    tmp:="{\\rm " cat nam cat "}_2&" cat Sprint(#subg) cat "&" 
    cat Sprint(Degree(grp)) cat "&" cat Sprint(#mat) cat "&" cat "\\\\\\hline" cat "\n";
    str cat:=tmp;
end for;
str;

nam:="McL";
G:=ATLASGroup(nam);
prk:=PermRepKeys(G);
str:="";
for p in [1..4] do  
    grp:=PermutationGroup(prk[p]);   
    subg:=Stabilizer(grp,1);
    ChiefFactors(subg);
    time mat:=PermutationConstituents(grp,subg);
    tmp:="{\\rm " cat nam cat "}_2&" cat Sprint(#subg) cat "&" cat 
    Sprint(Degree(grp)) cat "&" cat Sprint(#mat) cat "&" cat "\\\\\\hline" cat "\n";
    str cat:=tmp;
end for;
str;

uu:=ATLASGroupNames();
for nam in uu do
    G:=ATLASGroup(nam);
    prk:=PermRepKeys(G);
    str:="";
    for p in prk do
        if Degree(p) lt 10000 then  
                grp:=PermutationGroup(p);   
                subg:=Stabilizer(grp,1);
                ChiefFactors(subg);
                time mat:=PermutationConstituents(grp,subg);
                tmp:="{\\rm " cat nam cat "}&" cat Sprint(#subg) 
            cat "&" cat Sprint(Degree(grp)) cat "&" cat Sprint(#mat) 
            cat "&" cat "\\\\\\hline" cat "\n";
                str cat:=tmp;
        end if;
    end for;
    str;
end for;

nam:="Tra(20,546)";
grp:=TransitiveGroup(20,546);
maxt:=MaximalSubgroups(grp);
subg:=maxt[1]`subgroup;
time mat:=PermutationConstituents(grp,subg);
tmp:="{\\rm " cat nam cat "}&" cat Sprint(#subg) 
cat "&" cat Sprint(Degree(grp)) cat "&" cat Sprint(#mat) 
cat "&" cat "\\\\\\hline" cat "\n";
str cat:=tmp;

nam:="Per(122)";
DB:=PerfectGroupDatabase();
T:=Group(DB,122);
H:=sub<T|[T.1,T.2]>;
ca:=CosetAction(T,H);
grp:=ca(T);
subg:=ca(H);
time mat:=PermutationConstituents(grp,subg);
tmp:="{\\rm " cat nam cat "}&" cat Sprint(#subg) 
cat "&" cat Sprint(Degree(grp)) cat "&" cat Sprint(#mat) 
cat "&" cat "\\\\\\hline" cat "\n";
str cat:=tmp;

nam:="AS(98)";
DB:=AlmostSimpleGroupDatabase();
T:=GroupData(DB,98);
grp:=T`permrep;
maxt:=MaximalSubgroups(grp);
subg:=maxt[1]`subgroup;
time mat:=PermutationConstituents(grp,subg);
tmp:="{\\rm " cat nam cat "}&" cat Sprint(#subg) 
cat "&" cat Sprint(Degree(grp)) cat "&" cat Sprint(#mat) 
cat "&" cat "\\\\\\hline" cat "\n";
str cat:=tmp;

nam:="Pri(625,345)";
grp:=PrimitiveGroup(625,345);
maxt:=MaximalSubgroups(grp);
subg:=maxt[1]`subgroup;
time mat:=PermutationConstituents(grp,subg);
tmp:="{\\rm " cat nam cat "}&" cat Sprint(#subg) 
cat "&" cat Sprint(Degree(grp)) cat "&" cat Sprint(#mat) 
cat "&" cat "\\\\\\hline" cat "\n";
str cat:=tmp;

nam:="AS(198)";
DB:=AlmostSimpleGroupDatabase();
T:=GroupData(DB,198);
grp:=T`permrep;
maxt:=MaximalSubgroups(grp);
subg:=maxt[3]`subgroup;
time mat:=PermutationConstituents(grp,subg);
tmp:="{\\rm " cat nam cat "}&" cat Sprint(#subg) 
cat "&" cat Sprint(Degree(grp)) cat "&" cat Sprint(#mat) 
cat "&" cat "\\\\\\hline" cat "\n";
str cat:=tmp;


///////////////////////////////////////////////////////////////////////
//we prove that the structure constants are preserved under
//(i,j,k)->(j',i',k'), where dcr[i]^-1\in orbs[i] and these are the only
//elements of C_2 wr Sym(3) with such property
////////////////////////////////////////////////////////////////////////

grp:=PrimitiveGroup(125,34);
maxt:=MaximalSubgroups(grp);
subg:=maxt[1]`subgroup;

ca:=CosetAction(grp,subg);
G1:=ca(grp);

base := Base( G1 );
if base[1] ne 1 then
    ChangeBase( ~G1,[1] );
    base := Base( G1 );
end if;
Gf,fG:=FPGroupStrong(G1);

H1:=ca(subg);
orbset:=Orbits(H1);
orbs:=[Sort([x:x in o]):o in orbset];
minreps:=[Min(x):x in orbs];

dcr:=[];
for m in minreps do
    b,x:=IsConjugate(G1,1,m);
    dcr:=Append(dcr,x@@fG);
end for;
ndcr:=#dcr;
Hf,fH:=FPGroupStrong(H1);
invo:=Sym(#orbs)![dcd[1^fG(dcr[j]^-1)]:j in [1..#dcr]];
pp:=function(i,j,k)
        return #(orbset[i] meet orbset[j^invo]^fG(dcr[k]));
end function;

F:=Rationals();
R:=MatrixAlgebra(F,ndcr);
GenIntersectionMatrix:=function(j)
    return R![pp(i,j,k):i,k in [1..ndcr]];
end function;

V:=RSpace(F,ndcr);
b:=Basis(V);
Dlis:=[R!1];
D:=sub<R|Dlis>;
VD:=sub<V|V.1>;
poslis:=[2..ndcr];
repeat
    bvd:=Basis(VD);
    poslis:=[i:i in poslis|not b[i] in VD];
    minpos:=Minimum(poslis);
    Dlis:=Append(Dlis,R!GenIntersectionMatrix(minpos));
    D:=sub<R|Dlis>;
    VD:=sub<V|[b*d:b in bvd, d in Dlis]>;
    dim:=Dimension(VD);
    dim;
until dim eq ndcr;
bd:=Basis(D);
Orbs:=Orbits(H1);
C:=CartesianPower([1..#Orbs],3);
B:=CartesianPower([0..1],3);
inv:=Sym(#Orbs)![Position(Orbs,(1^fG(d)^-1)^H1):d in dcr];
SS:=Sym(3);
[<e,ss>:e in B,ss in SS|&and[bd[l[1^ss]^(inv^e[1]),l[2^ss]^(inv^e[2]),
l[3^ss]^(inv^e[3])] eq bd[l[1],l[2],l[3]]:l in C]];