|
################################################################################
##<#GAPDoc Label="SCNrRegularTorus">
## <ManSection>
## <Func Name="SCNrRegularTorus" Arg="n"/>
## <Returns>an integer upon success, <K>fail</K> otherwise.</Returns>
## <Description>
## Returns the number of simplicial regular maps on the torus with <M>n</M> vertices,
## cf. <Cite Key="Brehm08EquivMapsTorus"/> for details.
## <Example><![CDATA[
## gap> SCNrRegularTorus(9);
## gap> SCNrRegularTorus(10);
## ]]></Example>
## </Description>
## </ManSection>
##<#/GAPDoc>
################################################################################
InstallGlobalFunction(SCNrRegularTorus,
function(n)
if not IsPosInt(n) or n < 7 then
return fail;
fi;
if IsSquareInt(n) or IsSquareInt(3*n) then
return 1;
else
return 0;
fi;
end);
################################################################################
##<#GAPDoc Label="SCNrChiralTori">
## <ManSection>
## <Func Name="SCNrChiralTori" Arg="n"/>
## <Returns>an integer upon success, <K>fail</K> otherwise.</Returns>
## <Description>
## Returns the number of simplicial chiral maps on the torus with <M>n</M> vertices,
## cf. <Cite Key="Brehm08EquivMapsTorus"/> for details.
## <Example><![CDATA[
## gap> SCNrChiralTori(7);
## gap> SCNrChiralTori(343);
## ]]></Example>
## </Description>
## </ManSection>
##<#/GAPDoc>
################################################################################
InstallGlobalFunction(SCNrChiralTori,
function(n)
local factors,p,q,b,numSurfs,pSet,qSet,elm;
if not IsPosInt(n) or n < 7 then
return fail;
fi;
factors:=FactorsInt(n);
p:=Filtered(factors,x->x mod 6 = 1);
q:=Filtered(factors,x->x mod 6 = 5);
b:=[];
qSet:=Set(q);
Add(b,Size(Filtered(factors,x->x=2)));
for elm in qSet do
Add(b,Size(Filtered(q,x->x=elm)));
od;
if p = [] or ForAny(b,x->IsOddInt(x)) then
return 0;
fi;
pSet:=Set(p);
numSurfs:=1;
for elm in pSet do
numSurfs:=numSurfs*(Size(Filtered(p,x->x=elm))+1);
od;
return Int(1/2*numSurfs);
end);
SCIntFunc.PermList:=function(list)
local elm,j,pList,tmpList,p;
if not ForAll(list,x->IsDuplicateFreeList(x)) then
return fail;
fi;
tmpList:=[];
for elm in list do
Append(tmpList,elm);
od;
if not IsDuplicateFreeList(tmpList) then
return fail;
fi;
pList:=[];
for elm in list do
tmpList:=[1..Maximum(elm)];
for j in [1..Size(elm)-1] do
tmpList[elm[j]]:=elm[j+1];
od;
tmpList[elm[Size(elm)]]:=elm[1];
Add(pList,PermList(tmpList));
od;
p:=();
for elm in pList do
p:=p*elm;
od;
return p;
end;
################################################################################
##<#GAPDoc Label="SCSeriesSymmetricTorus">
## <ManSection>
## <Func Name="SCSeriesSymmetricTorus" Arg="p, q"/>
## <Returns>a <K>SCSimplicialComplex</K> object upon success, <K>fail</K> otherwise.</Returns>
## <Description>
## Returns the equivarient triangulation of the torus <M>\{ 3,6 \}_{(p,q)}</M> with
## fundamental domain <M>(p,q)</M> on the <M>2</M>-dimensional integer lattice.
## See <Cite Key="Brehm08EquivMapsTorus"/> for details.
## <Example><![CDATA[
## gap> c:=SCSeriesSymmetricTorus(2,1);
## gap> SCFVector(c);
## ]]></Example>
## </Description>
## </ManSection>
##<#/GAPDoc>
################################################################################
InstallGlobalFunction(SCSeriesSymmetricTorus,
function(p,q)
local phi,psi,sigma,x,y,verts,a,b,n,v,imv,i,j,elm,6cycle,3cycle,2cycle,done,idx,mat,trig,G,c;
# generators of automorphism group
psi:=[[-1,-1,1],[1,0,0],[0,0,1]];
phi:=[[0,-1,0],[1,1,0],[0,0,1]];
if q=0 then
sigma:=[[0,-1,p],[-1,0,p],[0,0,1]];
elif p=q then
sigma:=[[1,0,0],[-1,-1,3*p],[0,0,1]];
else
sigma:=[[1,0,0],[0,1,0],[0,0,1]];
fi;
# vertices
verts:=[];
n:=q^2+p*q+p^2;
for x in [-q..p-1] do
for y in [0..p+2*q-1] do
a:=(p+q)*x+q*y;
b:=-q*x+p*y;
if a < 0 or b < 0 or a >= n or b >= n then continue; fi;
Add(verts,[x,y]);
od;
od;
# permuations
# phi: rotation around origin
6cycle:=[];
idx:=0;
for i in [1..n] do
done:=false;
for elm in 6cycle do
if verts[i] in elm then done:=true; break; fi;
od;
if done then continue; fi;
v:=[[verts[i][1]],[verts[i][2]],[1]];
idx:=idx+1;
6cycle[idx]:=[];
mat:=[[1,0,0],[0,1,0],[0,0,1]];
for j in [1..6] do
imv:=mat*v;
mat:=mat*phi;
if not [imv[1][1],imv[2][1]] in verts then
a:=(p+q)*imv[1][1]+q*imv[2][1];
b:=-q*imv[1][1]+p*imv[2][1];
while a < 0 do
imv[1][1]:=imv[1][1]+(p);
imv[2][1]:=imv[2][1]+(q);
a:=(p+q)*imv[1][1]+q*imv[2][1];
od;
while a >= n do
imv[1][1]:=imv[1][1]+(-p);
imv[2][1]:=imv[2][1]+(-q);
a:=(p+q)*imv[1][1]+q*imv[2][1];
od;
while b < 0 do
imv[1][1]:=imv[1][1]+(-q);
imv[2][1]:=imv[2][1]+(p+q);
b:=-q*imv[1][1]+p*imv[2][1];
od;
while b >= n do
imv[1][1]:=imv[1][1]+(q);
imv[2][1]:=imv[2][1]+(-p-q);
b:=-q*imv[1][1]+p*imv[2][1];
od;
fi;
if not [imv[1][1],imv[2][1]] in verts then
Info(InfoSimpcomp,2,"SCSeriesSymmetricTorus: error in vertices.");
return fail;
fi;
if [imv[1][1],imv[2][1]] in 6cycle[idx] then
break;
fi;
Add(6cycle[idx],[imv[1][1],imv[2][1]]);
od;
od;
# psi: rotation around the center of a triangle
3cycle:=[];
idx:=0;
for i in [1..n] do
done:=false;
for elm in 3cycle do
if verts[i] in elm then done:=true; break; fi;
od;
if done then continue; fi;
v:=[[verts[i][1]],[verts[i][2]],[1]];
idx:=idx+1;
3cycle[idx]:=[];
mat:=[[1,0,0],[0,1,0],[0,0,1]];
for j in [1..3] do
imv:=mat*v;
mat:=mat*psi;
if not [imv[1][1],imv[2][1]] in verts then
a:=(p+q)*imv[1][1]+q*imv[2][1];
b:=-q*imv[1][1]+p*imv[2][1];
while a < 0 do
imv[1][1]:=imv[1][1]+(p);
imv[2][1]:=imv[2][1]+(q);
a:=(p+q)*imv[1][1]+q*imv[2][1];
od;
while a >= n do
imv[1][1]:=imv[1][1]+(-p);
imv[2][1]:=imv[2][1]+(-q);
a:=(p+q)*imv[1][1]+q*imv[2][1];
od;
while b < 0 do
imv[1][1]:=imv[1][1]+(-q);
imv[2][1]:=imv[2][1]+(p+q);
b:=-q*imv[1][1]+p*imv[2][1];
od;
while b >= n do
imv[1][1]:=imv[1][1]+(q);
imv[2][1]:=imv[2][1]+(-p-q);
b:=-q*imv[1][1]+p*imv[2][1];
od;
fi;
if not [imv[1][1],imv[2][1]] in verts then
Info(InfoSimpcomp,2,"SCSeriesSymmetricTorus: error in vertices.");
return fail;
fi;
if [imv[1][1],imv[2][1]] in 3cycle[idx] then
break;
fi;
Add(3cycle[idx],[imv[1][1],imv[2][1]]);
od;
od;
# sigma: reflection (only in regular case)
2cycle:=[];
idx:=0;
for i in [1..n] do
done:=false;
for elm in 2cycle do
if verts[i] in elm then done:=true; break; fi;
od;
if done then continue; fi;
v:=[[verts[i][1]],[verts[i][2]],[1]];
idx:=idx+1;
2cycle[idx]:=[];
mat:=[[1,0,0],[0,1,0],[0,0,1]];
for j in [1..2] do
imv:=mat*v;
mat:=mat*sigma;
if not [imv[1][1],imv[2][1]] in verts then
a:=(p+q)*imv[1][1]+q*imv[2][1];
b:=-q*imv[1][1]+p*imv[2][1];
while a < 0 do
imv[1][1]:=imv[1][1]+(p);
imv[2][1]:=imv[2][1]+(q);
a:=(p+q)*imv[1][1]+q*imv[2][1];
od;
while a >= n do
imv[1][1]:=imv[1][1]+(-p);
imv[2][1]:=imv[2][1]+(-q);
a:=(p+q)*imv[1][1]+q*imv[2][1];
od;
while b < 0 do
imv[1][1]:=imv[1][1]+(-q);
imv[2][1]:=imv[2][1]+(p+q);
b:=-q*imv[1][1]+p*imv[2][1];
od;
while b >= n do
imv[1][1]:=imv[1][1]+(q);
imv[2][1]:=imv[2][1]+(-p-q);
b:=-q*imv[1][1]+p*imv[2][1];
od;
fi;
if not [imv[1][1],imv[2][1]] in verts then
Info(InfoSimpcomp,2,"SCSeriesSymmetricTorus: error in vertices.");
return fail;
fi;
if [imv[1][1],imv[2][1]] in 2cycle[idx] then
break;
fi;
Add(2cycle[idx],[imv[1][1],imv[2][1]]);
od;
od;
# triangle of map
trig:=[[0,0],[1,0],[0,1]];
for i in [1,2,3] do
if not trig[i] in verts then
a:=(p+q)*trig[i][1]+q*trig[i][2];
b:=-q*trig[i][1]+p*trig[i][2];
while a < 0 do
trig[i][1]:=trig[i][1]+(p);
trig[i][2]:=trig[i][2]+(q);
a:=(p+q)*trig[i][1]+q*trig[i][2];
od;
while a >= n do
trig[i][1]:=trig[i][1]+(-p);
trig[i][2]:=trig[i][2]+(-q);
a:=(p+q)*trig[i][1]+q*trig[i][2];
od;
while b < 0 do
trig[i][1]:=trig[i][1]+(-q);
trig[i][2]:=trig[i][2]+(p+q);
b:=-q*trig[i][1]+p*trig[i][2];
od;
while b >= n do
trig[i][1]:=trig[i][1]+(q);
trig[i][2]:=trig[i][2]+(-p-q);
b:=-q*trig[i][1]+p*trig[i][2];
od;
fi;
od;
trig:=[Position(verts,trig[1]),Position(verts,trig[2]),Position(verts,trig[3])];
trig:=Set(trig);
# map vertices to integers 1,2,...
for i in [1..Size(6cycle)] do
for j in [1..Size(6cycle[i])] do
6cycle[i][j]:=Position(verts,6cycle[i][j]);
od;
od;
for i in [1..Size(3cycle)] do
for j in [1..Size(3cycle[i])] do
3cycle[i][j]:=Position(verts,3cycle[i][j]);
od;
od;
for i in [1..Size(2cycle)] do
for j in [1..Size(2cycle[i])] do
2cycle[i][j]:=Position(verts,2cycle[i][j]);
od;
od;
# convert lists to permutations
2cycle:=SCIntFunc.PermList(2cycle);
3cycle:=SCIntFunc.PermList(3cycle);
6cycle:=SCIntFunc.PermList(6cycle);
G:=Group([2cycle,3cycle,6cycle]);
c:=SCFromGenerators(G,[trig]);
SCRename(c,Concatenation("{3,6}_(",String(p),",",String(q),")"));
SetSCTopologicalType(c,"T^2");
SetSCAutomorphismGroup(c,G);
return c;
end);
################################################################################
##<#GAPDoc Label="SCRegularTorus">
## <ManSection>
## <Func Name="SCRegularTorus" Arg="n"/>
## <Returns>a <K>SCSimplicialComplex</K> object upon success, <K>fail</K> otherwise.</Returns>
## <Description>
## Returns a list of regular triangulations of the torus with <M>n</M> vertices (the
## length of the list will be at most <M>1</M>).
## See <Cite Key="Brehm08EquivMapsTorus"/> for details.
## <Example><![CDATA[
## gap> cc:=SCRegularTorus(9);
## gap> g:=SCAutomorphismGroup(cc[1]);
## gap> SCNumFaces(cc[1],0)*12 = Size(g);
## ]]></Example>
## </Description>
## </ManSection>
##<#/GAPDoc>
################################################################################
InstallGlobalFunction(SCRegularTorus,
function(n)
local p,q;
if SCNrRegularTorus(n) = fail then
return fail;
elif SCNrRegularTorus(n) = 0 then
return [];
fi;
if IsSquareInt(n) then
p := Sqrt(n);
q := 0;
elif IsSquareInt(3*n) then
p := Sqrt(n/3);
q := Sqrt(n/3);
else
return fail;
fi;
return [SCSeriesSymmetricTorus(p,q)];
end);
################################################################################
##<#GAPDoc Label="SCChiralTori">
## <ManSection>
## <Func Name="SCChiralTori" Arg="n"/>
## <Returns>a <K>SCSimplicialComplex</K> object upon success, <K>fail</K> otherwise.</Returns>
## <Description>
## Returns a list of chiral triangulations of the torus with <M>n</M> vertices.
## See <Cite Key="Brehm08EquivMapsTorus"/> for details.
## <Example><![CDATA[
## gap> cc:=SCChiralTori(91);
## gap> SCIsIsomorphic(cc[1],cc[2]);
## ]]></Example>
## </Description>
## </ManSection>
##<#/GAPDoc>
################################################################################
InstallGlobalFunction(SCChiralTori,
function(n)
local p,q,list,done,l,m;
l := SCNrChiralTori(n);
if SCNrChiralTori(n) = fail then
return fail;
elif l = 0 then
return [];
fi;
done:=false;
list:=[];
for q in [1..n] do
for p in [q+1..n] do
m:=p*p + p*q + q*q;
if m < n then
continue;
elif m = n then
Add(list,SCSeriesSymmetricTorus(p,q));
if Size(list) >= l then
done:=true;
break;
fi;
elif m > n then
break;
fi;
od;
if done = true then
break;
fi;
od;
return list;
end);
################################################################################
##<#GAPDoc Label="SCRegularMaps">
## <ManSection>
## <Func Name="SCRegularMaps" Arg=""/>
## <Returns>a list of lists upon success, <K>fail</K> otherwise.</Returns>
## <Description>
## Returns a list of all simplicial (hyperbolic) regular maps of orientable genus up to <M>100</M>
## or non-orientable genus up to <M>200</M>. The list was generated with the help of
## the classification of regular maps by Marston Conder <Cite Key="Conder09RegMapsOfBdChi"/>.
##
## Every regular map is given by a <M>3</M>-tuple <M>(m,g,or)</M> where <M>m</M> is the
## vertex valence, <M>g</M> is the genus and <M>or</M> is a boolean stating if the
## map is orientable or not.
##
## Use the <M>3</M>-tuples of the list together with <Ref Func="SCRegularMap"/>
## to get the corresponding triangulations.
## <M>g</M>
## <Example><![CDATA[
## gap> ll:=SCRegularMaps(){[1..10]};
## gap> c:=SCRegularMap(ll[5][1],ll[5][2],ll[5][3]);
## gap> SCHomology(c);
## gap> SCGenerators(c);
## ]]></Example>
## </Description>
## </ManSection>
##<#/GAPDoc>
################################################################################
InstallGlobalFunction(SCRegularMaps,
function()
local mg;
mg:=[[7,3,true],[7,7,true],[7,8,false],[7,14,true],
[7,15,false],[7,147,false],[8,3,true],[8,5,true],
[8,8,true],[8,9,false],[8,16,true],[8,17,true],
[8,17,false],[8,22,true],[8,23,false],[8,33,true],
[8,46,true],[8,47,false],[8,52,true],[8,65,true],
[8,82,true],[8,85,true],[8,86,false],[9,10,true],
[9,15,true],[9,16,false],[9,43,true],[9,69,true],
[9,70,false],[9,96,true],[9,97,false],[10,6,true],
[10,13,true],[10,14,false],[10,25,true],[10,26,true],
[10,26,false],[10,45,true],[10,46,false],[10,49,true],
[10,65,true],[10,73,true],[10,74,false],[10,89,true],
[10,116,false],[10,134,false],[10,170,false],
[11,26,true],[12,10,true],[12,13,true],[12,25,true],
[12,28,true],[12,29,false],[12,33,true],[12,37,true],
[12,49,true],[12,56,true],[12,57,false],[12,65,true],
[12,73,true],[12,76,true],[12,82,true],[12,92,true],
[12,93,false],[12,97,true],[13,50,true],[13,51,false],
[14,15,true],[14,49,true],[14,99,true],[14,106,false],
[14,146,false],[15,37,true],[15,73,true],[15,76,true],
[16,21,true],[16,41,true],[16,81,true],[17,134,false],
[18,28,true],[18,82,true],[18,170,false],[20,36,true],
[20,85,true],[20,86,false],[20,177,false],[22,45,true],
[24,55,true],[24,73,true],[26,66,true],[28,78,true],
[30,91,true]];
return mg;
end);
################################################################################
##<#GAPDoc Label="SCRegularMap">
## <ManSection>
## <Func Name="SCRegularMap" Arg="m, g, orient"/>
## <Returns>a <K>SCSimplicialComplex</K> object upon success, <K>fail</K> otherwise.</Returns>
## <Description>
## Returns the (hyperbolic) regular map of vertex valence <Arg>m</Arg>, genus <Arg>g</Arg> and orientability
## <Arg>orient</Arg> if existent and <K>fail</K> otherwise.
##
## The triangulations were generated with the help of
## the classification of regular maps by Marston Conder <Cite Key="Conder09RegMapsOfBdChi"/>.
##
## Use <Ref Func="SCRegularMaps"/> to get a list of all regular maps available.
## <Example><![CDATA[
## gap> SCRegularMaps(){[1..10]};
## gap> c:=SCRegularMap(7,7,true);
## gap> g:=SCAutomorphismGroup(c);
## gap> Size(g);
## ]]></Example>
## </Description>
## </ManSection>
##<#/GAPDoc>
################################################################################
InstallGlobalFunction(SCRegularMap,
function(m,g,orient)
local autGroups,gens,n,f2,G,mg,i,c;
if not IsPosInt(m) or m < 7 or not IsInt(g) and g >= 2 then
Info(InfoSimpcomp,1,"SCRegularMap: argument 1 must be an integer > 6, argument 2 must be an integer > 1.");
return fail;
fi;
if not orient in [true, false] then
Info(InfoSimpcomp,1,"SCRegularMap: argument 3 must be true or false.");
return fail;
fi;
mg:=[];
gens:=[];
autGroups:=[];
if not orient then
n:=6*(2-g)/(6-m);
f2:= 2*m*(2-g)/(6-m);
autGroups[1]:=
[ ( 1,24)( 2,22)( 4,16)( 5,23)( 6,10)( 7,26)( 8,25)( 9,28)(11,19)(12,31)
(14,35)(15,34)(18,27)(20,30)(21,29)(32,33),
( 1,36,18, 4,15,32,17)( 2, 8,33,27,11,14,20)( 3,26,23,22,10,25,16)
( 5,30,12,29, 9, 7,21)( 6,35,31,28,13,34,19) ];
autGroups[2]:=
[ ( 1, 6)( 2, 8)( 3,10)( 4,17)( 7,12)( 9,20)(11,19)(14,15)(16,21),
( 1, 9,15,17,14, 3,16, 7)( 2,11,21, 5,10,20,18, 6)( 8,12,19,13) ];
autGroups[3]:=
[ ( 1, 2,15,16,18, 6, 4,21)( 3,20, 9,14,17, 5, 7,13)( 8,12,19,10),
( 1, 9, 5)( 2, 7,20,21,15, 4)( 3, 8,10,13,16, 6)(11,12,14,18,17,19) ];
autGroups[4]:=[ ( 2, 5)( 4, 6)( 7,18)( 8,15)( 9,16)(10,14)(11,13)(12,17),
( 1,11,16, 4,12,14, 6, 7,13, 3,10,15, 2, 8,17)( 5, 9,18) ];
autGroups[5]:=
[ ( 1,20,41,19,22,64,68,73,70,53,33,12,56)( 2,16,69,45,28,60, 4,39,43,35,77,
55, 3)( 5,47,24,76,40,21,44, 8,52,11, 7,30,59)( 6,54,31,26,38,65,63,71,
78,74,46,29,37)( 9,61,58,14,32,67,42,36,57,13,72,51,17)(10,27,62,66,75,
48,23,34,15,49,25,50,18), ( 1,33,29,11, 8, 6)( 2,21,30,35, 9,17)
( 3,27,28,38, 7,22)( 4,12,31)( 5,24,32,26,10,39)(13,37,14,23,15,25)
(16,20,19,34,36,18)(40,70,41,59,72,58)(42,46,51,55,61,54)(43,75,67,49,73,
53)(44,71,60,62,77,68)(45,74,56)(47,76,69,66,78,57)(48,64,50,65,52,63) ];
autGroups[6]:=
[ ( 1, 3,10)( 2,12,17)( 4,25,26)( 5, 6,22)( 7,16,15)( 8,13,23)( 9,18,20)
(11,21,28)(14,24,19), ( 1,24,21,10, 3,15,14)( 2,12,11, 8,27, 6, 7)
( 4,20, 5,13,25, 9,17)(16,28,18,23,19,22,26) ];
autGroups[7]:=
[ ( 1, 9,39,24, 3,14,43,19)( 2,15,40,22, 4,12,32,25)( 6,45,37,20,13,26,33,18)
( 7,21,11,17)( 8,41,29,23,10,36,44,16)(27,28,31,38,35,30,42,34),
( 1,16,37,11, 4,21,36, 6)( 3,22,34,10, 5,20,31,12)( 7,19,42,39,15,23,26,35)
( 8,18,14,24)( 9,17,30,29,13,25,43,38)(27,28,40,44,33,41,45,32) ];
autGroups[8]:=
[ ( 1,12,18, 3)( 2, 7,10,15, 5,14,11,13)( 4,17,21, 9, 8,19,16, 6)
(22,45,24,60,34,53,35,47)(23,55,39,54,40,50,29,51)(25,48,36,52)
(26,57,27,58,37,61,33,43)(28,44,30,63)(31,49,42,59,41,62,38,46)(32,56),
( 1,39, 2,42, 4,36)( 3,31,10,28, 7,24)( 5,33,17,27,13,30)( 6,26, 9,38,12,34)
( 8,32,16,41,19,35)(11,40,20,29,14,37)(15,23,18,25,21,22)(43,63,44,57,46,
60)(45,49,52)(47,48,59,51,55,54)(50,62,58,56,61,53) ];
autGroups[9]:=
[ ( 2,10)( 3,15)( 4,22)( 6,14)( 7,17)( 8,24)(12,13)(16,34)(18,30)(19,31)
(20,35)(21,36)(23,29)(26,33)(27,32),
( 1,24,36,29,16,19,32, 8)( 2, 6,12,26)( 3,33,13, 4, 7,27,21,17)
( 5, 9,10,20,23,31,18,14)(11,22,30,25,34,28,35,15) ];
autGroups[10]:=
[ ( 1, 9, 5)( 2, 3, 6, 4, 7, 8)(10,23,13,24,16,22)(11,20,14,21,17,19)
(12,26,15,27,18,25), ( 1,25,18, 9,24,14, 5,20,10)( 2,26,16, 7,22,15, 6,21,
11)( 3,27,17, 8,23,13, 4,19,12) ];
autGroups[11]:=
[ ( 1,38,27,55)( 2,39,41,32)( 3,11,36,49)( 4,52,18,66)( 5,53,62,64)
( 6,54,43,46)( 7,40,24,35)( 8,19,13,50)( 9,16,37,23)(10,21,30,59)
(12,51,29,61)(14,63,42,33)(15,58,17,26)(20,44,57,31)(22,28,56,25)(34,60)
(45,47)(48,65), ( 1,46,39,31,37)( 2,29,50,51,41, 3,48,63,60,24)
( 4,20,30,35,36, 8,64,54,45,56)( 5,47,44,25,13, 7,49,52,43,59)
( 6,34,15,22,27, 9,62,58,65,57)(10,26,16,32,38,17,66,11,33,40)
(12,14,28,23,21,18,55,53,42,61) ];
autGroups[12]:=
[ ( 1,24,17,25,64,31,62,32,52,51, 4,59)( 2,57,14,23,65, 6,60,15,28,48,39,66)
( 3,58,13,29,34,43,50,35,63, 7,54,20)( 5,19,12,27,42,44,38,33,49,46,55,11)
( 8,40,21,22,61,41,56,37, 9,47,18,30)(10,36,16,26,53,45),
( 1,26,36,17,30,35,61,66,39, 9,50,40)( 2,48,59,18,28,38,42,11,46,57,21,25)
( 3,32,58,20,23,33,64,45, 4,49,60,13)( 5,14,24,15,27,37,53,63,56,43,10,41)
( 6, 7,47,19,12,22,34,65,55,52,62,44)( 8,51,54,16,29,31) ];
autGroups[13]:=
[ ( 1, 46, 67, 40,131, 57,118,126, 90, 35)( 2, 75,128, 42,116, 20,135, 15,
59,117)( 3, 74, 14, 41,110, 38,112,103, 88,102)( 4, 72,127, 6, 50,
54, 44,125, 91,115)( 5, 58,108, 36,109, 56,107, 79, 23, 80)
( 7, 49, 65, 43, 84,101, 82, 99, 83,100)( 8, 17, 69, 12, 60,130, 39,124,
92,121)( 9, 26, 48, 37, 98,134,120,113, 24,132)( 10, 73, 89, 45, 13, 70,
111, 11, 71,104)( 16, 68, 97, 63,114, 22,133,129, 32, 28)
( 18, 52, 96, 62,106, 55, 25, 81,105, 31)( 19, 66, 93, 30, 51, 53, 94, 87,
122, 33)( 21, 78, 77, 61, 76)( 27, 47, 64, 95, 86,119, 85,123, 34, 29),
( 1,103, 96, 31,130,135, 27, 70, 94, 6,134,107, 33, 89,133)
( 2,125,105, 55,110,132, 16, 73, 93, 36,131,121, 53, 71,123)
( 3,126, 5, 79,108, 80, 48, 74, 47, 41, 95, 42, 86, 88, 85)
( 4, 15, 77, 76,117, 69, 46, 49, 43, 40, 63,120, 82, 83, 24)
( 7, 92, 25, 8,128, 78, 28,104, 68, 26,101, 44, 30, 91,118)
( 9, 56,109, 35, 54, 75, 29, 38, 98, 32, 57,112, 34, 20,124)
( 10, 87, 23,113, 14, 81, 18,102, 67, 58, 51, 45, 64, 59,119)
( 11, 97, 61,114,111, 66, 17, 99, 12, 62,106,115, 65, 72, 19)
( 13,129, 21,116,127, 52, 50,100, 37, 60,122, 39, 84, 90, 22) ];
autGroups[14]:=
[ ( 1,35,24,32, 5,40, 7)( 2,34,14,13,33, 4,26)( 3, 6,16,23,30,19,39)
( 8,38,42, 9,22,10,15)(11,20,41,17,25,21,18)(12,29,37,31,27,36,28),
( 1,41,15,30, 8,14)( 2, 5,22,40,37,16)( 3,25,42,12,39,24)( 4,17,26,32,31,23)
( 6,38, 7)( 9,36,34,28,19,21)(10,13,35,11,29,20)(18,27,33) ];
autGroups[15]:=
[ ( 2, 5,17,12, 4, 7,19,13, 3, 6,18,11)( 8,20,29,14, 9,21,31,16,10,22,30,15)
(23,27,36,42,50,52,44,54,48,39,33,24)(25,26,35,41,51,46,55,53,45,47,38,32)
(28,37,43,49,40,34), ( 1,28,21,41,32, 4,30, 5,55,35,14,40)( 2,52,17,25,46,
12,24, 7,31,23,50,29)( 3,53,20,47,45,16,38, 6,54,37,49,39)
( 8,44,36,33,10,13,26,22,43,15,51,18)( 9,19,27,34,42,11) ];
autGroups[16]:=
[ ( 1,14,44,31,30, 4)( 2,46,41,19,50,47)( 3,22,43)( 5,12,21,48, 7,40)
( 6, 9,36,53, 8,17)(10,29,15,33,37,42)(11,34,54,45,24,39)(13,28,26)
(16,38,27,25,55,51)(18,23,20,52,49,32), ( 1,42, 5,49)( 2,31)( 3,33, 8,24)
( 4,29,25, 6)( 7,48,13,22)( 9,40,50,37)(10,55)(11,14,38,28)(12,51,17,18)
(15,32,27,54)(16,19,21,30)(23,34,41,43)(26,47,45,52)(35,44,39,53)(36,46)
];
autGroups[17]:=
[ ( 1, 16,124, 79, 38,110,101, 20, 71)( 2, 93, 31, 75, 57, 44,122, 83, 7)
( 3, 26,128, 61, 43,113, 96, 27, 4)( 5, 13,126,134, 62,105,116,131, 82)
( 6, 12, 76, 32,127, 64, 41,112, 97)( 8, 47, 65,136, 73, 92, 48,104, 98)
( 9, 23, 95, 10, 19, 99, 25, 17, 58)( 11, 56, 30,133, 63,130,106,114,100)
( 14, 69, 87, 55,108,117,107, 81, 37)( 15, 78, 86, 46,115,102, 18, 59, 29)
( 21, 70, 33, 53, 77,129,111, 90, 42)( 22, 68, 60, 45,121, 84, 35, 91, 49)
( 28, 54, 66, 39,123, 80, 52,103, 94)( 34, 40,125,135, 72,118,132, 85, 36)
( 50,109,119, 67,120, 74, 88, 51, 89), ( 1, 80, 35, 31, 43, 78, 12, 96)
( 2, 97, 5, 84, 52,134, 46,124)( 3, 90, 36, 28, 41, 63, 53,122)
( 4, 83, 7, 79, 38,128, 19, 95)( 6, 86, 62,127, 23, 99, 59, 82)
( 8,129, 72,133,112, 93, 91, 98)( 9, 64, 54, 20)( 10, 61, 75, 17, 24,
58, 71, 27)( 11,102, 60,135,111, 26,110, 70)( 13,114, 37, 88, 48,125,
45,121)( 14,116, 65,120,132, 30,118, 74)( 15,113, 76, 81,100, 33,130, 73
)( 16,115, 56, 85, 42, 87, 55,123)( 18, 25, 57, 68)( 21,101, 66,119,107,
32,105, 69)( 22, 44, 77, 47,131, 29, 92, 51)( 34,117, 67,136,106,126,
103, 94)( 39,108, 40,104, 49, 89, 50,109) ];
autGroups[18]:=
[ ( 1, 3, 49, 44, 22, 18, 55, 27)( 2, 35, 74, 31, 26, 19,108, 41)
( 4, 20, 15, 67, 58, 88, 51, 5)( 6, 70, 85, 21)( 7, 90, 29, 16, 47,
57, 99, 37)( 8, 11, 32, 76, 89, 87, 65, 52)( 9, 38, 66, 13, 23, 83,
82, 68)( 10, 14, 92, 60)( 12, 25, 43, 64,104, 80, 24, 30)
( 17, 62, 33, 97,100, 78, 63, 56)( 28, 95, 53, 59, 93, 61, 81, 46)
( 34, 98, 69, 73, 40,106,107, 36)( 39, 54, 94,103, 71, 96, 48, 42)
( 45, 86,101, 91, 77, 79,102, 50)( 72, 75, 84,105),
( 1, 24,100, 89, 31, 41, 52, 63,104, 44)( 2, 48,103, 45, 61, 66, 30, 79,
83, 15)( 3, 14, 47, 23, 59, 95, 90, 38, 70, 49)( 4, 7, 86, 64, 16,
46,102, 34,106, 74)( 5, 88, 67, 22, 21, 68, 91, 99, 60, 27)
( 6, 94, 93, 62, 28, 98, 92, 11, 19, 32)( 8, 65, 33, 58, 13, 37,105, 96,
71, 85)( 9, 84, 40, 97, 53, 56, 42, 75, 57, 25)( 10, 36,107, 72, 82, 29,
51, 17, 87, 76)( 12, 55, 20, 18, 43, 26, 73, 81, 39,108)( 50, 80)
( 54, 78, 69, 77,101) ];
autGroups[19]:=
[ ( 1, 90,173, 77,151, 69,128, 45,251, 76,233, 81)( 2, 89,174, 78,152, 70,
127, 46,252, 75,234, 82)( 3,113,237,108,241, 29, 92,105,199,115,217,124)
( 4,114,238,107,242, 30, 91,106,200,116,218,123)( 5,175,248,167,243,169,
6,176,247,168,244,170)( 7, 11,206,185, 73,149,211,165,197,109,227,156)
( 8, 12,205,186, 74,150,212,166,198,110,228,155)( 9,103, 57,177, 38, 33,
48, 23,214, 96, 66, 14)( 10,104, 58,178, 37, 34, 47, 24,213, 95, 65, 13)
( 15,129,139, 17, 56, 51, 16,130,140, 18, 55, 52)( 19,239,145,189,138,236,
20,240,146,190,137,235)( 21,231,179,216,194, 36,183, 60,131,144, 93,226)
( 22,232,180,215,193, 35,184, 59,132,143, 94,225)( 25, 42,220, 64, 98,172,
26, 41,219, 63, 97,171)( 27,221,118, 83,100, 62,121, 80,181, 39,153,203)
( 28,222,117, 84, 99, 61,122, 79,182, 40,154,204)( 31,133,102, 68,141, 43,
126,245,164,210,250, 88)( 32,134,101, 67,142, 44,125,246,163,209,249, 87)
( 49,191,187,224,230, 54, 50,192,188,223,229, 53)( 71,201,158,159,111,195,
72,202,157,160,112,196)( 85,147,208,162,135,119, 86,148,207,161,136,120),
( 1,144, 53,251, 62,190, 99,242, 50,131, 4, 86,150,214,202, 31, 44,159,
177,197,119)( 2,143, 54,252, 61,189,100,241, 49,132, 3, 85,149,213,201,
32, 43,160,178,198,120)( 5, 28, 35, 63,118,209,135,234, 38,188, 34, 48,
224, 24,238,147,163, 80, 97, 21, 40)( 6, 27, 36, 64,117,210,136,233, 37,
187, 33, 47,223, 23,237,148,164, 79, 98, 22, 39)( 7,157, 11,134,169,115,
232,239,123, 74,192,114, 82,230,110, 89,235,194, 77,176,142)
( 8,158, 12,133,170,116,231,240,124, 73,191,113, 81,229,109, 90,236,193,
78,175,141)( 9, 51,103,200,220,102,221,161,184, 84,196,121,225,208,182,
67,171,151, 66, 56, 14)( 10, 52,104,199,219,101,222,162,183, 83,195,122,
226,207,181, 68,172,152, 65, 55, 13)( 15,185, 46,146, 94, 76, 71,250,211,
167,166,246,112,107, 59,137, 29,228, 18,105, 70)( 16,186, 45,145, 93, 75,
72,249,212,168,165,245,111,108, 60,138, 30,227, 17,106, 69)
( 19,154,217,140,179, 92, 41,155, 58,248,126, 88,244, 96,205, 25,128,215,
130,173,204)( 20,153,218,139,180, 91, 42,156, 57,247,125, 87,243, 95,206,
26,127,216,129,174,203) ];
autGroups[20]:=
[ ( 2, 3, 5, 8,12,16,20,26,30,33,35,34,32,28,24,19,15,11, 7, 4)
( 6, 9,13,14,10)(17,21,22,18)(23,27,31,29,25),
( 1, 2, 3)( 4, 6, 5)( 7,11, 9)( 8,10,12)(13,15,17)(14,18,16)(19,23,21)
(20,22,25)(24,28,27)(26,29,30)(31,32,33)(34,36,35),
( 2, 3)( 4, 5)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)
(23,25)(24,26)(27,29)(28,30)(32,33)(34,35) ];
autGroups[21]:=
[ ( 1,52,80, 8,10,49,38)( 2,62,89,13,17,91,56)( 3,32,60,25, 5,75,76)
( 4,21,46,35,20, 9,85)( 6,57,84,39,14,77,82)( 7,54,31,59,19,41,18)
(11,70,23,44,36,40,22)(12,65,79,72,43,87,34)(15,86,53,26,63,33,83)
(16,74,51,50,45,37,90)(24,69,55,27,73,48,42)(28,71,61,47,58,68,67)
(29,64,88,30,66,78,81), ( 1,57,33,41,88,79, 6,46,10, 4,24,90)
( 2,78,21,61,73,68,23,64,39,52,45,60)( 3, 8,84,81,29,62)( 5,63,38,20,77,
12,11,87,35,72,91,22)( 7,50,82,74,58, 9,30,40,47,16,17,37)
(13,65,66,31,26,89,25,51,69,44,76,70)(14,49,75,56,86,71,19,43,34,59,67,15)
(18,27,83,32,36,42,55,85,80,53,48,54) ];
autGroups[22]:=
[ ( 1, 8,71,74,68,69,45,43,82,51,27,14)( 2,20, 7,79,64,89,39,87,42,52,32,16)
( 3,78,72,53,29,24)( 4,31,19,11,65,75,44,67,84,37,33,21)( 5,58,57,61,56,
62,38,60,59,47,28,17)( 6,80,40,86,66,54,26,22, 9,50,30,23)
(10,77,49,34,18,12,41,73,83,48,35,15)(13,81,76,90,70,91,46,88,85,55,36,25)
, ( 1,70)( 2,65)( 3,64)( 4,68)( 5,67)( 7,39)( 8,29)( 9,69)(10,56)(11,48)
(12,66)(13,18)(14,81)(15,76)(16,90)(17,88)(19,46)(20,36)(21,91)(22,63)
(23,55)(24,85)(26,71)(27,79)(28,78)(30,41)(32,80)(33,58)(34,50)(35,77)
(37,74)(38,73)(42,75)(43,57)(44,49)(45,72)(47,86)(51,89)(52,61)(54,83)
(59,87)(62,82) ];
autGroups[23]:=
[ ( 1, 48, 90,127, 22, 76,134,143,125,155,118,178,175, 13,180,100, 6,150, 91
)( 2,131, 89, 16,156,144, 70,149,117,154, 54,179,174, 29, 5,185, 87,
120, 99)( 3, 43, 46,140, 85, 80, 37, 33, 56, 62,147,164,163,115,168,170,
190,108, 95)( 4, 26, 74,186,129,124,130,157,146,160, 19,116,176, 69,148,
181, 94, 9, 98)( 7, 81, 92, 34, 12, 58,133, 65,152,159,142, 52,177,113,
24, 75,182, 40,101)( 8,109, 93,167, 38,136,128, 82,106, 36,145, 59, 44,
119,161, 83,102, 32, 97)( 10,137, 88, 79,103, 30,132, 41,138,158, 86,105,
31,114, 57,172,112,162, 96)( 11, 39,139, 68, 20,104, 35, 50, 60,173, 27,
55,184,188, 28, 71,183,110,123)( 14, 25, 73, 63,151,126,166, 53,189,171,
18, 72,111, 66,121, 42,141, 51, 84)( 15,122, 61, 67,153,165, 17, 49,169,
64, 23, 78,187, 47, 45,135, 21, 77,107),
( 1, 62)( 2, 63)( 3, 41)( 4, 56)( 5, 57)( 6, 58)( 7, 61)( 9, 60)
( 10, 59)( 11, 42)( 12, 91)( 13,104)( 14,117)( 15,126)( 16,173)( 17,159)
( 18, 78)( 19,165)( 20,181)( 21,111)( 22, 95)( 23,108)( 25,112)( 26,109)
( 27, 36)( 28,110)( 29,103)( 30, 65)( 31,164)( 32,153)( 33, 93)( 34,147)
( 35,158)( 37,119)( 38, 96)( 39,182)( 40,121)( 44,167)( 45, 47)( 46,132)
( 48, 98)( 49,179)( 50, 90)( 51,169)( 52,189)( 53,184)( 54, 84)( 55,177)
( 64, 76)( 66,124)( 67,186)( 68,144)( 69, 80)( 70,136)( 72,190)( 73, 88)
( 74, 97)( 75, 82)( 77,170)( 79,172)( 81,185)( 85,100)( 86,175)( 87,122)
( 89,145)( 92,114)( 94,156)(101,129)(102,116)(105,115)(106,113)(107,118)
(120,151)(123,143)(125,188)(127,138)(128,139)(130,135)(131,137)(133,140)
(134,141)(142,160)(146,171)(148,180)(149,162)(152,174)(155,166)(157,187)
(161,176)(168,178) ];
autGroups[24]:=
[ ( 1,136, 2,103, 43, 57,135, 21,145)( 3,154, 20,102, 8, 61, 54, 24,125)
( 4,146, 52,109,134, 58,175, 33,140)( 5, 90, 40, 86, 88, 56, 99, 23, 89)
( 6,126, 38,112, 26, 60, 19, 28, 44)( 7,148, 50,107, 74, 62,189, 34,144)
( 9, 10, 45, 41,101, 59, 70, 37, 27)( 11,152, 51,111,113, 64,184, 32, 75)
( 12,147, 47,105,128, 63,169, 30,138)( 13,150, 49, 72,127, 68,187, 36,114)
( 14, 76, 46,110,132, 69,124, 31,141)( 15,149, 39,104,133, 67,190, 25,139)
( 16,153, 42,106,131, 65, 85, 29,143)( 17,151, 53,100,129, 66,180, 22,137)
( 18,115, 48,108,130, 55,162, 35,142)( 71, 91, 97, 96, 98, 87, 93, 95, 94)
( 73,156,182,177, 84,116,173,181,179)( 77,160,185,186,123,118,171,176, 80)
( 78,155,167,166,168,117,163,165,164)( 79,158,178, 82,161,122,172,183,119)
( 81,157, 83,159,188,121,174,120,170),
( 1,150)( 2,149)( 3,153)( 4,154)( 5,146)( 6,126)( 7,152)( 8,103)
( 9,151)( 11, 90)( 12,148)( 13,147)( 14, 45)( 15, 28)( 16,136)( 17,115)
( 18, 61)( 19, 76)( 20,176)( 21,183)( 22,184)( 23,158)( 24,131)( 25,182)
( 26,108)( 27,181)( 29, 95)( 30,171)( 31,165)( 32, 50)( 34,141)( 35,120)
( 36, 66)( 37, 81)( 38,179)( 39,180)( 40,157)( 41,130)( 42,178)( 43,107)
( 44,177)( 46, 94)( 47,170)( 48,164)( 51,140)( 52,119)( 53, 65)( 54, 80)
( 55,190)( 56,161)( 57,134)( 58,188)( 59,111)( 60,186)( 62, 98)( 63,174)
( 64,168)( 67,144)( 68,123)( 70, 84)( 71,162)( 72,135)( 73,189)( 74,112)
( 75,187)( 77, 99)( 78,175)( 79,169)( 82,145)( 83,124)( 86,127)( 87,160)
( 88,104)( 89,159)( 92,156)( 93,155)( 96,137)( 97,116)(100,133)(102,132)
(105,129)(106,128)(109,125)(110,113)(114,185)(117,173)(118,167)(121,143)
(138,172)(139,166) ];
autGroups[25]:=
[ ( 1,21,17, 5,70,69,44)( 2,48,66,71,42, 8,74)( 3,28,39,36,20,16,38)
( 4,35,78,29,11,34,27)( 6,58,60,75,54,52,12)( 7,37,64,63,10,23,15)
( 9,43,22,13,30,46,33)(14,73,19,18,72,65,24)(25,59,31,47,49,45,67)
(26,53,32,62,40,56,41)(50,76,55,61,57,51,68),
( 1,66,45,56,73,72,25,26,74,63,52,54)( 2,37,40,16,23,24,69,46,59,17,48,58)
( 3,75,14,62,68,31,65,12,13,36,77, 9)( 4,30,19,28,15,53,42,49,70,22,18,38)
( 5,35,27, 7,41,29,50,20,33,51,11,67)( 6,10,34,71, 8,78,44,60,47,55,61,32)
(21,64,76,39,43,57) ];
autGroups[26]:=
[ ( 1,25,66,38,65,37)( 2,56,73,69,60,19)( 3,13,47,63,78,54)( 4,31,59)
( 5,68,45)( 6,70,64,10,41,28)( 7,35,77,50,75,43)( 8,44,62,71,49,11)
( 9,51,23,33,36,15)(12,26,46,20,17,72)(14,57,32,34,55,39)(16,74,24,29,58,
27)(18,52,76,53,22,67)(21,42,40,30,48,61),
( 1,77,55,51,71,64, 2,62,54,25,69,76)( 3,57,78,70, 5,53)( 4,39,17,33,52,10,
7,26,34,31,38, 8)( 6,24,11,15,75,65,16,22,12,13,63,72)( 9,73,43,28,61,
74,21,67,36,56,50,59)(14,47,32,66,27,45,19,58,60,68,29,44)
(18,37,42,48,49,41,30,35,20,46,23,40) ];
autGroups[27]:=
[ ( 1, 8,70,50, 4, 2,25,74,18, 3, 5,42,66,11)( 6,13,20,10,29, 7,45)
( 9,38,77,17,21,16,72,63,12,32,27,73,52,15)(14,19,26,56,40,24,23,41,28,47,
30,33,44,37)(22,35,55,57,69,36,48,58,43,53,31,62,67,59)(34,71,46,75,65,
39,64,49,78,60,54,51,61,76), ( 1,16,56,49,15,78,57)( 2,20,27,58,65,43,14)
( 3,30,76,51,37,18,39)( 4,59,53,36,11,71,60)( 5,25,42,74,63,61,32)
( 6,41,38,26,45, 8,70)( 7,13,77,19,55,28, 9)(10,44,67,34,54,48,33)
(17,75,23,73,50,35,46)(21,40,69,68,22,24,52)(29,66,47,31,64,62,72) ];
autGroups[28]:=
[ ( 1, 34)( 2, 98)( 3,152)( 4,107)( 5,150)( 6, 30)( 8, 33)( 9, 27)
( 10, 42)( 11,139)( 12,102)( 13,140)( 14,151)( 15,138)( 16, 83)( 17,118)
( 18, 59)( 19,120)( 20, 40)( 21,146)( 22,143)( 23,167)( 24,128)( 25,166)
( 26, 32)( 28, 35)( 36, 50)( 37, 94)( 38, 97)( 39, 44)( 41, 56)( 43,105)
( 46, 81)( 47,119)( 48,108)( 49,116)( 51, 63)( 52, 82)( 53,117)( 54,114)
( 55,115)( 57,132)( 58,109)( 60, 66)( 61, 93)( 62, 95)( 64, 92)( 65, 89)
( 67,145)( 68, 86)( 69,144)( 70, 90)( 71, 72)( 73, 80)( 74, 78)( 76, 79)
( 84, 96)( 85, 91)( 87,125)( 88,123)( 99,170)(100,134)(101,165)(103,121)
(104,160)(110,124)(111,159)(112,137)(113,130)(122,141)(127,129)(131,153)
(133,142)(135,158)(136,163)(147,171)(148,149)(154,162)(155,157)(164,168),
( 1, 89, 13, 60,147)( 2, 72,108, 56,155)( 3, 86,141, 27, 96)
( 4, 90, 33, 46,169)( 5, 40,136, 59,104)( 6, 92,115, 58, 21)
( 7, 95,148, 28, 52)( 8, 51,161, 48,149)( 9, 98,131, 61,111)
( 10,145, 63, 26, 93)( 11,144,120, 47,168)( 12,143,117, 57,162)
( 14, 83, 99, 29, 44)( 15,146,135, 49,152)( 16, 75,106, 70, 31)
( 17, 87,142,124,165)( 18, 42,133, 82,101)( 19, 55,140,122,171)
( 20, 73, 62, 78,109)( 22, 74,107,123,157)( 23, 36,100,116, 45)
( 24, 88,138,121,160)( 25, 41,139,114, 84)( 30, 91, 65, 76, 66)
( 32, 94,125, 85, 69)( 34, 97,164, 37,110)( 35, 50,156, 64, 77)
( 38,112,119,105,127)( 39,113, 81,102,132)( 43,154,118,103,150)
( 53,153,163,170,158)( 54,151,134,159,126)( 67, 71, 79, 68, 80)
(128,129,167,137,166) ];
autGroups[29]:=
[ ( 1, 14, 36, 13, 57, 56, 47, 66, 43, 22, 6, 25)( 2, 62, 31, 16, 42, 24)
( 3, 53, 33, 20, 51, 55, 40, 29, 4, 61, 32, 17)( 5, 45, 28, 10, 63, 34,
18, 65, 46, 59, 44, 26)( 7, 50, 37, 19, 27, 9, 58, 35, 12, 64, 41, 23)
( 8, 11, 38, 15, 21, 54, 52, 60, 48, 49, 39, 30)( 67,182,120,151, 76,195,
122,171, 81,183,131,148)( 68,157,107,173, 78,168,128,137,103,180, 93,150)
( 69,146, 75,177, 79,174, 86,196,101,181,102,144)( 70,170,119,138, 82,197,
95,191, 99,158,108,145)( 71,194, 90,172, 84,159,110,187, 97,163,129,142)
( 72,185,112,164, 80,135,132,198, 94,179,123,149)( 73,193,100,175, 87,153)
( 74,190,118,162, 85,186,114,169,104,136,130,152)( 77,143,121,176, 83,189,
126,154, 98,178,117,147)( 88,192, 89,155,106,156,109,166,116,133,127,139)
( 91,134,125,161, 96,184,113,160,111,141,115,167)( 92,165,124,140,105,188)
, ( 1,186,126, 19,148,105, 53,180, 90, 65,133,102, 5,159,128, 17,193,
115, 58,176, 74, 36,166, 99, 39,149,111, 24,182,112, 60,138, 69)
( 2,174, 73, 15,187,125, 45,152, 96, 54,163,100, 66,140,129, 8,195,114,
18,171, 71, 38,188, 89, 42,147, 98, 55,158,119, 29,143,117)
( 3,168,101, 16,154,127, 25,194, 92, 57,164, 67, 37,156,124, 30,146,109,
52,175, 75, 35,141,123, 6,153,110, 13,181,121, 62,139, 93)
( 4,189, 86, 12,191, 82, 50,192, 83, 51,165, 81, 49,155, 80, 26,190, 78,
47,172, 76, 31,184, 84, 43,150, 85, 46,179, 79, 48,134, 87)
( 7,135,131, 10,196,132, 14,198, 88, 63,167, 94, 64,160,104, 22,157,116,
23,177, 70, 33,173, 68, 32,145,106, 41,144,107, 56,136,120)
( 9,183,122, 20,137,130, 11,197, 95, 21,169,103, 61,161, 91, 27,170, 97,
59,162, 77, 28,185,113, 40,151, 72, 34,178,118, 44,142,108) ];
autGroups[30]:=
[ ( 1,23,10,47)( 2,24,11,48)( 3,21,12,45)( 4,22, 9,46)( 5,15,44,36)
( 6,16,41,33)( 7,13,42,34)( 8,14,43,35)(17,71,37,55)(18,72,38,56)
(19,69,39,53)(20,70,40,54)(25,61,29,49)(26,62,30,50)(27,63,31,51)
(28,64,32,52)(57,59)(58,60)(65,67)(66,68),
( 1,28,68,70,17,63,38,16)( 2,25,65,71,18,64,39,13)( 3,26,66,72,19,61,40,14)
( 4,27,67,69,20,62,37,15)( 5, 6, 7, 8)( 9,58,36,54,32,24,43,47)
(10,59,33,55,29,21,44,48)(11,60,34,56,30,22,41,45)(12,57,35,53,31,23,42,46
)(49,52,51,50) ];
autGroups[31]:=
[ ( 1, 47, 9, 63, 30, 55, 11, 40, 25, 56, 33, 64, 23, 44)( 2, 38, 17, 49,
36, 45, 18, 37, 4, 42, 19, 52, 26, 41)( 3, 54, 35, 69, 22, 53, 29, 43,
15, 66, 24, 57, 12, 50)( 5, 65, 28, 60, 6, 46, 34, 51, 31, 71, 27, 48,
7, 58)( 8, 70, 16, 59, 20, 72, 14, 61, 21, 68, 13, 62, 32, 67)
( 10, 39)( 73, 84, 95,104, 92, 87, 76)( 74, 80, 98, 96,107, 85, 97)
( 75, 93, 90, 86,102,105, 89)( 77,100, 99,106, 78,103, 82)
( 81, 88,101, 83, 94,108, 91), ( 1, 77, 42, 29,101, 48, 36,102, 55)
( 2, 86, 66, 18, 83, 62, 10, 94, 72)( 3, 96, 56, 27, 90, 59, 19,108, 69)
( 4, 80, 58, 11,106, 64, 26, 78, 46)( 5, 91, 49, 16, 99, 43, 33, 98, 60)
( 6,104, 71, 23, 74, 54, 17,103, 67)( 7, 73, 47, 34, 97, 57, 30, 92, 53)
( 8, 81, 39, 21, 88, 37, 31,100, 41)( 9,105, 51, 13, 95, 68, 24, 82, 63)
( 12, 75, 38, 25, 93, 44, 22,107, 45)( 14, 89, 52, 28, 85, 40, 15, 84, 50)
( 20, 79, 70, 32, 76, 65, 35, 87, 61) ];
autGroups[32]:=
[ ( 1,127,718,867,346,586,841)( 2,128,717,868,345,585,842)( 3,466,779,360,
785,588,105)( 4,465,780,359,786,587,106)( 5,277,387,866,781,572,852)
( 6,278,388,865,782,571,851)( 7,468,609,823,669,567,556)
( 8,467,610,824,670,568,555)( 9,368,777,809,696,591,211)
( 10,367,778,810,695,592,212)( 11,477,769,109,150,574,858)
( 12,478,770,110,149,573,857)( 13,488,764,710,792,185,309)
( 14,487,763,709,791,186,310)( 15,410,430,445,432,416,441)
( 16,409,429,446,431,415,442)( 17,470,776,793,579,590, 50)
( 18,469,775,794,580,589, 49)( 19,452,508,523,510,493,519)
( 20,451,507,524,509,494,520)( 21,229,740,626,783,570,651)
( 22,230,739,625,784,569,652)( 23,482, 38,486,762,593,789)
( 24,481, 37,485,761,594,790)( 25,475,668,655,545,236,751)
( 26,476,667,656,546,235,752)( 27,453,249,756,611,584,679)
( 28,454,250,755,612,583,680)( 29,459,543,266,742,566,819)
( 30,460,544,265,741,565,820)( 31,484,200,313,389,596,805)
( 32,483,199,314,390,595,806)( 33,489,344,836,787, 79,159)
( 34,490,343,835,788, 80,160)( 35,458,766,684,642,530,262)
( 36,457,765,683,641,529,261)( 39,455,771, 53,472,577,854)
( 40,456,772, 54,471,578,853)( 41,463,774,216,300,374,856)
( 42,464,773,215,299,373,855)( 43,462,639,559,251,576,621)
( 44,461,640,560,252,575,622)( 45,480, 93,163,719,597,356)
( 46,479, 94,164,720,598,355)( 47, 73,148,733,798,330,831)
( 48, 74,147,734,797,329,832)( 51,179,297,404,796,581,705)
( 52,180,298,403,795,582,706)( 55,473,694,859,201,283,400)
( 56,474,693,860,202,284,399)( 57,324,767,846, 96,134,729)
( 58,323,768,845, 95,133,730)( 59,144,737,363,352,829,103)
( 60,143,738,364,351,830,104)( 61,120,384,869,348,702,843)
( 62,119,383,870,347,701,844)( 63,145,605,827,336,648,554)
( 64,146,606,828,335,647,553)( 65,124,736,814,337,834,209)
( 66,123,735,813,338,833,210)( 67,156,728,113,121,725,849)
( 68,155,727,114,122,726,850)( 69,166,721,713,357,208,307)
( 70,165,722,714,358,207,308)( 71,126,425,450,321,438,440)
( 72,125,426,449,322,437,439)( 75,130,504,527,325,516,518)
( 76,129,503,528,326,515,517)( 77,118,716,630,349,675,649)
( 78,117,715,629,350,676,650)( 81,154,663,659,328,257,749)
( 82,153,664,660,327,258,750)( 83,132,245,759,332,815,678)
( 84,131,246,760,331,816,677)( 85,138,540,270,341,617,818)
( 86,137,539,269,342,618,817)( 87,161,195,317,320,837,803)
( 88,162,196,318,319,838,804)( 89,167,339,840,353,101,157)
( 90,168,340,839,354,102,158)( 91,135,723,688,333,551,259)
( 92,136,724,687,334,552,260)( 97,142,731,219,272,396,847)
( 98,141,732,220,271,395,848)( 99,140,636,563,224,748,619)
(100,139,635,564,223,747,620)(107,116,293,408,362,802,704)
(108,115,294,407,361,801,703)(111,152,689,864,174,305,397)
(112,151,690,863,173,306,398)(169,296,376,825,671,633,557)
(170,295,375,826,672,634,558)(171,273,405,812,698,707,213)
(172,274,406,811,697,708,214)(175,315,392,711,808,193,311)
(176,316,391,712,807,194,312)(177,276,366,448,433,423,443)
(178,275,365,447,434,424,444)(181,279,370,526,512,502,521)
(182,280,369,525,511,501,522)(183,221,386,628,800,661,653)
(184,222,385,627,799,662,654)(187,304,379,657,548,244,754)
(188,303,380,658,547,243,753)(189,281,225,758,613,700,682)
(190,282,226,757,614,699,681)(191,287,371,267,743,604,821)
(192,288,372,268,744,603,822)(197,286,394,685,644,537,263)
(198,285,393,686,643,538,264)(203,292,401,217,302,381,862)
(204,291,402,218,301,382,861)(205,290,377,562,253,691,623)
(206,289,378,561,254,692,624)(227,428,418,435,421,419,414)
(228,427,417,436,422,420,413)(231,505,496,513,499,498,492)
(232,506,495,514,500,497,491)(233,247,607,616,674,631,534)
(234,248,608,615,673,632,533)(237,745,602,645,536,239,542)
(238,746,601,646,535,240,541)(241,637,532,256,666,599,550)
(242,638,531,255,665,600,549),
( 1,825,126,317,467,331,382,186,232,810,732,639,676,841,546)
( 2,826,125,318,468,332,381,185,231,809,731,640,675,842,545)
( 3,870,428,271,367,187,244,582,503,776,682,651,786,103,549)
( 4,869,427,272,368,188,243,581,504,775,681,652,785,104,550)
( 5,267,434,293,470,602,706,579, 76,824,161,660,747,353,372)
( 6,268,433,294,469,601,705,580, 75,823,162,659,748,354,371)
( 7,811,426,297,461,622,696, 80,513,164,863,638,352,397,183)
( 8,812,425,298,462,621,695, 79,514,163,864,637,351,398,184)
( 9,488,417,292,456,495,709,592,497,836,844,533, 46,847,413)
( 10,487,418,291,455,496,710,591,498,835,843,534, 45,848,414)
( 11,406,177,221,474,606,694,570,519,793,107,645,156,849,541)
( 12,405,178,222,473,605,693,569,520,794,108,646,155,850,542)
( 13,217,228,301,465,610,662,590,510,110,821,137,839,749,328)
( 14,218,227,302,466,609,661,589,509,109,822,138,840,750,327)
( 15,315,410,286,464,566,502,593,521,655,833,649,552, 47,562)
( 16,316,409,285,463,565,501,594,522,656,834,650,551, 48,561)
( 17,627,424,283,452,626,707,568,515,846,557, 28,837,440,281)
( 18,628,423,284,451,625,708,567,516,845,558, 27,838,439,282)
( 19,866,444,287,478,619,538, 23,526,446,312,459,618,704,529)
( 20,865,443,288,477,620,537, 24,525,445,311,460,617,703,530)
( 21, 55,447,275,277,457,603,571,494,524,860,653,648,829,554)
( 22, 56,448,276,278,458,604,572,493,523,859,654,647,830,553)
( 25,712,415,279,486,624,634,585,518,560, 51,658,437,307,453)
( 26,711,416,280,485,623,633,586,517,559, 52,657,438,308,454)
( 29,855,431, 66,475,135,713,575,325,404,214,240,801,728,544)
( 30,856,432, 65,476,136,714,576,326,403,213,239,802,727,543)
( 31,595,412,314,484,600,702,587,492, 54,862,419,305,480,531)
( 32,596,411,313,483,599,701,588,491, 53,861,420,306,479,532)
( 33,778,421,310,471, 82,700,134,528,755,358,377,207,260,548)
( 34,777,422,309,472, 81,699,133,527,756,357,378,208,259,547)
( 35,361,366,172,230,614,689,577,500,853,791, 84,816,157,564)
( 36,362,365,171,229,613,690,578,499,854,792, 83,815,158,563)
( 37,685,441,300, 73,616,142,598,505,359,402,189,258,803,540)
( 38,686,442,299, 74,615,141,597,506,360,401,190,257,804,539)
( 39,111,435,119,489,607,338,374,181,266,807,636,768,678,556)
( 40,112,436,120,490,608,337,373,182,265,808,635,767,677,555)
( 41,735,429,289,482,611, 88,584,130,868,753,333,396,209,234)
( 42,736,430,290,481,612, 87,583,129,867,754,334,395,210,233)
( 43,165,450,296,324,376,193,235,511,733,774,632,832,787, 78)
( 44,166,449,295,323,375,194,236,512,734,773,631,831,788, 77)
( 49,796, 72,303,128,630,692,329,370,216,264,644,726,769,535)
( 50,795, 71,304,127,629,691,330,369,215,263,643,725,770,536)
( 57,758,321,273,180,237,698,573,508,683,852,642,101,818,131)
( 58,757,322,274,179,238,697,574,507,684,851,641,102,817,132)
( 59,827,146,364,386,174,226,203,245,764,663,771,669,105,784)
( 60,828,145,363,385,173,225,204,246,763,664,772,670,106,783)
( 61,255,151,738,740,336,400,202, 63,800,143,779,665,356,390)
( 62,256,152,737,739,335,399,201, 64,799,144,780,666,355,389)
( 67,393,116,269,743,340,388,191,262,781, 89,766,139,858,741)
( 68,394,115,270,744,339,387,192,261,782, 90,765,140,857,742)
( 69,206,118,813,715,344,379,212,251, 98,724,147,688,751,345)
( 70,205,117,814,716,343,380,211,252, 97,723,148,687,752,346)
( 85,820,150,114,746,121,407,197,223,392,195,250,671,729,761)
( 86,819,149,113,745,122,408,198,224,391,196,249,672,730,762)
( 91,350,123,220,248,347,384,199,241,806,719, 94,673,160,798)
( 92,349,124,219,247,348,383,200,242,805,720, 93,674,159,797)
( 95, 99,154,168,759,342,319,176,170,254,721,717,668,679,789)
( 96,100,153,167,760,341,320,175,169,253,722,718,667,680,790) ];
autGroups[33]:=
[ ( 1, 89, 33,155,125, 3, 94, 34,156,121)( 2, 95, 30,149,126, 4, 91, 26,
148,122)( 5, 88, 32,151,124, 6, 96, 36,154,123)( 7, 85, 25,147,130,
8, 93, 29,150,129)( 9, 90, 35,153,131, 11, 86, 31,152,127)
( 10, 87, 27,145,132, 12, 92, 28,146,128)( 13, 73,102,236,165, 47,221,211,
64, 49)( 14, 77, 98,231,166, 48,217,214, 62, 51)( 15, 81,105,237,157, 39,
222,208, 63, 50)( 16, 82,106,239,161, 42,218,216, 61, 52)
( 17, 74,101,235,162, 41,226,215, 67, 55)( 18, 78, 97,229,158, 40,225,209,
68, 56)( 19, 79,108,240,167, 45,220,212, 65, 53)( 20, 83,104,234,163, 44,
219,206, 66, 54)( 21, 75, 99,230,164, 43,227,205, 72, 57)
( 22, 76,100,232,168, 46,223,213, 70, 59)( 23, 80,107,238,159, 37,228,207,
71, 58)( 24, 84,103,233,160, 38,224,210, 69, 60)(109,136,175,185,197,115,
137,179,190,193)(110,134,176,184,196,112,133,171,192,195)
(111,135,169,191,198,116,138,177,187,194)(113,139,172,186,203,118,142,180,
182,199)(114,140,170,183,204,120,141,174,188,200)(117,144,178,181,202,
119,143,173,189,201)(241,248,246,244,250)(243,252,245,247,249),
( 1,223, 13,139)( 2,226, 14,133)( 3,220, 17,140)( 4,228, 18,135)
( 5,227, 15,143)( 6,221, 16,141)( 7,224, 21,136)( 8,218, 22,134)
( 9,217, 19,142)( 10,225, 20,137)( 11,219, 23,144)( 12,222, 24,138)
( 25, 36)( 26, 35)( 27, 28, 29, 30)( 31, 34, 33, 32)( 37,208, 73,246)
( 38,216, 74,252)( 39,211, 77,249)( 40,214, 78,248)( 41,209, 75,243)
( 42,215, 76,251)( 43,206, 81,242)( 44,212, 82,250)( 45,207, 79,245)
( 46,210, 80,244)( 47,205, 83,241)( 48,213, 84,247)( 49, 60)( 50, 59)
( 51, 54, 53, 52)( 55, 56, 57, 58)( 61,202, 89,171)( 62,201, 90,179)
( 63,194, 88,176)( 64,198, 87,177)( 65,197, 85,174)( 66,193, 86,180)
( 67,204, 95,169)( 68,200, 96,175)( 69,199, 94,172)( 70,203, 93,173)
( 71,196, 91,170)( 72,195, 92,178)( 97,127, 99,128)( 98,124,100,122)
(101,130,102,132)(103,121,104,123)(105,131,107,129)(106,125,108,126)
(109,164,147,188)(110,165,148,189)(111,159,145,183)(112,167,146,191)
(113,168,150,192)(114,162,149,186)(115,163,152,187)(116,157,151,181)
(117,158,155,182)(118,166,156,190)(119,160,153,184)(120,161,154,185)
(229,240)(230,234,231,236)(232,237)(233,239,235,238) ];
autGroups[34]:=
[ ( 1,38,16,46,20,43,23,40,26,48, 6,49,17,39,27,42,19,55)( 2,36,14,50, 3,37,
9,53, 5,47, 8,56,25,32,21,44,24,31)( 4,51, 7,41,12,52,10,54,13,33,28,34,
18,30,22,35,15,45)(11,29)(57,82,84,58,71,67,63,65,69)(59,70,66,73,75,81,
62,83,74)(60,68,64,79,80,61,72,77,78),
( 1,53,67,24,48,78)( 2,41,68,18,47,73)( 3,39,61,20,32,57)( 4,46,59,17,33,69)
( 5,50,60,25,31,80)( 6,52,63,22,38,81)( 7,56,66,14,34,79)( 8,54,64,15,36,
83)( 9,44,77)(10,43,62,27,35,82)(11,49,76,16,29,65)(12,30,75)
(13,55,74,26,45,71)(19,42,58,23,40,84)(21,37,72)(28,51,70) ];
autGroups[35]:=
[ ( 1,20,53,73,74,45,15, 3,18,68,70,69,29, 8, 9,26,63,49,60,21)( 2,14,28,16)
( 4, 6,65,47,71,54,37,25,11,35,27,39,38,10,23,41,48,72,44,57)( 7,13,31,34)
(12,32,24,22,66,42,40,46,43,67)(17,51,58,52)(19,50,62,61)(30,56,59,33)
(36,55,75,64), ( 1,73,30,41,44,14,10,48,62, 9,49,13,42,43,31)
( 2,47,11,28, 6,68,17,53,12, 5,22,26,58,18,27)( 3,34,32,65,19,63, 4,16,39,
20,59,35,24, 7,70)( 8,61,57,66,36,72,21,52,60,23,64,67,38,33,74)
(15,71,55,46,45,51,29,40,75,25,69,50,54,37,56) ];
gens[1]:=[ 1, 16, 27 ];
gens[2]:=[ 1, 2, 5 ];
gens[3]:=[ 1, 4, 17 ];
gens[4]:=[ 1, 7, 13 ];
gens[5]:=[ 1, 4, 7 ];
gens[6]:=[ 1, 2, 12 ];
gens[7]:=[ 1, 2, 6 ];
gens[8]:=[ 1, 22, 43 ];
gens[9]:=[ 1, 2, 3 ];
gens[10]:=[ 1, 10, 19 ];
gens[11]:=[ 1, 2, 4 ];
gens[12]:=[ 1, 23, 38 ];
gens[13]:=[ 1, 2, 6 ];
gens[14]:=[ 1, 2, 3 ];
gens[15]:=[ 1, 2, 5 ];
gens[16]:=[ 1, 2, 3 ];
gens[17]:=[ 1, 2, 34 ];
gens[18]:=[ 1, 2, 3 ];
gens[19]:=[ 1, 4, 190 ];
gens[20]:=[ 1, 2, 3 ];
gens[21]:=[ 1, 2, 75 ];
gens[22]:=[ 1, 27, 67 ];
gens[23]:=[ 1, 2, 141 ];
gens[24]:=[ 1, 40, 102 ];
gens[25]:=[ 1, 3, 8 ];
gens[26]:=[ 1, 2, 3 ];
gens[27]:=[ 1, 2, 3 ];
gens[28]:=[ 1, 2, 6 ];
gens[29]:=[ 1, 72, 172 ];
gens[30]:=[ 1, 5, 17 ];
gens[31]:=[ 1, 37, 73 ];
gens[32]:=[ 1, 247, 500 ];
gens[33]:=[ 1, 13, 25 ];
gens[34]:=[ 1, 29, 57 ];
gens[35]:=[ 1, 2, 3 ];
mg[1]:=[ 7, 8 ];
mg[2]:=[ 8, 9 ];
mg[3]:=[ 8, 9 ];
mg[4]:=[ 10, 14 ];
mg[5]:=[ 7, 15 ];
mg[6]:=[ 9, 16 ];
mg[7]:=[ 8, 17 ];
mg[8]:=[ 8, 23 ];
mg[9]:=[ 10, 26 ];
mg[10]:=[ 12, 29 ];
mg[11]:=[ 10, 46 ];
mg[12]:=[ 10, 46 ];
mg[13]:=[ 8, 47 ];
mg[14]:=[ 13, 51 ];
mg[15]:=[ 12, 57 ];
mg[16]:=[ 12, 57 ];
mg[17]:=[ 9, 70 ];
mg[18]:=[ 10, 74 ];
mg[19]:=[ 8, 86 ];
mg[20]:=[ 20, 86 ];
mg[21]:=[ 12, 93 ];
mg[22]:=[ 12, 93 ];
mg[23]:=[ 9, 97 ];
mg[24]:=[ 9, 97 ];
mg[25]:=[ 14, 106 ];
mg[26]:=[ 14, 106 ];
mg[27]:=[ 14, 106 ];
mg[28]:=[ 10, 116 ];
mg[29]:=[ 10, 134 ];
mg[30]:=[ 17, 134 ];
mg[31]:=[ 14, 146 ];
mg[32]:=[ 7, 147 ];
mg[33]:=[ 10, 170 ];
mg[34]:=[ 18, 170 ];
mg[35]:=[ 20, 177 ];
else
n:=6*(2-2*g)/(6-m);
f2:= 2*m*(2-2*g)/(6-m);
autGroups[1]:=
[ ( 1,13,12, 3, 7,16)( 2,21,19)( 4,23, 8, 6,20, 9)( 5,15,18)(10,17,22,11,14,
24), ( 1,18,17)( 2,10, 4)( 3,20,22)( 5,12,23)( 6,24,15)( 7,11, 9)
( 8,16,21)(13,14,19) ];
autGroups[2]:=
[ ( 2, 3)( 4, 5)( 7, 8)(10,11), ( 1, 7, 6,11,12, 5, 9, 2)( 3,10) ];
autGroups[3]:=
[ ( 2, 3, 5, 8,14,12, 7, 4)( 6, 9,15,10)(11,16,20,13,19,23,22,17)(18,21),
( 1, 2, 3)( 4, 6, 5)( 7,11, 9)( 8,10,13)(12,18,16)(14,20,21)(15,17,19)
(22,24,23), ( 2, 3)( 4, 5)( 7, 8)( 9,10)(11,13)(12,14)(16,20)(17,19)
(18,21)(22,23) ];
autGroups[4]:=
[ ( 1, 5, 6, 2,12, 7,15,13, 9,11)( 3,14)( 4,10),
( 1,15, 6, 9,12)( 2,10,11, 8, 7, 4, 5,14,13, 3) ];
autGroups[5]:=
[ ( 1,41,55,34,49, 9,26,72,11,23,68,43,51,62)( 2,64,29,59,32,28, 4,70,18,37,
48,19,17,66)( 3,56,67,22,60,47,15,71,33,12,27,24,61,39)
( 5,46,57, 6,30,31,42,69,53, 7,65,52,40,35)( 8,14,44,20,13,16,50,63,
36,38,25,45,58,21)(10,54),
( 1,70, 3,65,13,25,39, 7,66)( 2,71, 6,45,20,15,57, 4,72)
( 5,41,16,68,49,38,62,12,54)( 8,64, 9,27,30,47,35,23,28)
(10,69,11,58,34,43,44,26,67)(14,56,31,48,60,53,21,37,19)
(17,63,18,51,22,52,61,42,55)(24,46,50,29,32,36,33,40,59) ];
autGroups[6]:=
[ ( 2, 3, 5, 8,14,12, 7, 4)( 6, 9,15,22,29,23,16,10)(11,17,24,31,26,20,13,18
)(19,21,27,34,41,40,32,25)(28,35,38,30,37,33,39,36),
( 1, 2, 3)( 4, 6, 5)( 7,11, 9)( 8,10,13)(12,19,17)(14,20,21)(15,18,16)
(22,23,28)(24,25,30)(26,33,27)(29,36,35)(31,38,39)(32,34,37)
(40,42,41), ( 2, 3)( 4, 5)( 7, 8)( 9,10)(11,13)(12,14)(15,16)(17,20)
(19,21)(22,23)(24,26)(25,27)(30,33)(32,34)(35,36)(38,39)(40,41) ];
autGroups[7]:=
[ ( 2, 3, 5, 8,14,12, 7, 4)( 6, 9,15,24,34,26,16,10)(11,17,27,21,13,20,28,18
)(19,22,30,39,33,37,38,29)(23,31,40,41,36,25,35,32),
( 1, 2, 3)( 4, 6, 5)( 7,11, 9)( 8,10,13)(12,19,17)(14,21,22)(15,18,23)
(16,25,20)(24,32,33)(26,37,35)(27,29,30)(28,36,31)(34,39,38)
(40,41,42), ( 2, 3)( 4, 5)( 7, 8)( 9,10)(11,13)(12,14)(15,16)(17,21)
(18,20)(19,22)(23,25)(24,26)(29,30)(31,36)(32,35)(33,37)(38,39)
(40,41) ];
autGroups[8]:=
[ ( 1,22,17)( 2,30, 3, 8,28,14,12,29, 7)( 4,10, 9, 5,15,31,20,32,16)
( 6,34,23,25,26,24,27,19,33)(11,35,13)(18,36,21),
( 1,27,21,25,18, 6)( 2,12,31, 9,33,24)( 3, 7,34,19,32,15)
( 4,11,20,36, 5,13)( 8,23,16)(10,26,14)(17,30,35,29,22,28) ];
autGroups[9]:=
[ ( 2, 3, 5, 8,11,14,17,16,13,10, 7, 4)( 6, 9)(12,15),
( 1, 2, 3)( 4, 6, 5)( 7, 8, 9)(10,12,11)(13,14,15)(16,18,17),
( 2, 3)( 4, 5)( 7, 8)(10,11)(13,14)(16,17) ];
autGroups[10]:=
[ ( 1, 6,15,19,32,36,29,28, 9,16)( 2,27,18,30,17,21,14, 3,26, 8)
( 4,20,25, 7,24,13,35,33,22,34)( 5,11)(10,23)(12,31),
( 1,17,23, 2, 9,33, 6, 5,28,13)( 4,25, 8,11,21)( 7,10,34,19,26,29,31,
15,14,36)(12,24,27,30,22)(16,18)(20,32) ];
autGroups[11]:=
[ ( 2, 3, 5, 8,14,20,23,22,17,12, 7, 4)( 6, 9,10)(11,15,18,13)(16,21,19),
( 1, 2, 3)( 4, 6, 5)( 7,11, 9)( 8,10,13)(12,16,15)(14,18,19)(17,20,21)
(22,24,23), ( 2, 3)( 4, 5)( 7, 8)( 9,10)(11,13)(12,14)(15,18)(16,19)
(17,20)(22,23) ];
autGroups[12]:=
[ ( 1, 90,109,118, 44, 82,100, 16, 84,115, 61, 78, 53, 95)( 2, 79, 37,146,
124,145, 43, 13,119,106,113,151, 68, 51)( 3, 57, 77, 83, 92,108, 66
)( 4, 48, 54,114, 58, 93,123, 30,111, 89,122,131, 75, 69)
( 5, 34,121, 56, 64,112, 91, 9, 22,152, 21,107, 81,130)
( 6,141, 40,127,150,116, 19)( 7,110, 96,134, 67, 45,149, 55,147,
63, 42,101, 33,128)( 8, 87, 86,104, 14, 60, 59, 31, 41,143, 35,
47, 36,137)( 10, 29, 62, 85,120,133, 80, 49, 76,140,156,125, 46, 17
)( 11,132, 12,136,135,154, 24, 20,142, 50, 98,144, 70, 28)
( 15, 74, 52,153, 38, 65,138, 72,117, 25, 99,126,105, 88)
( 18,102, 23,129,155,103, 71, 39,148, 97,139, 94, 26, 32)( 27, 73),
( 1,102, 44,110, 80, 60, 91, 11, 69, 98,101, 76, 31,121)
( 2,128, 64, 74, 49, 73, 59)( 3,132, 14, 48, 71, 87,100, 6, 95,
41, 32,111, 47,142)( 4,153, 92, 99, 30,143, 35, 18, 88,127,138,
39,104, 86)( 5, 79, 24, 90, 43, 34, 66, 22, 51, 84, 28,119, 9,141
)( 7,114,124, 65,103,112, 70, 33, 94,113,126, 89, 56,109)
( 8, 29, 67,136,123, 20,130, 36, 17,147, 78,148, 16,152)
( 10,117,107,149, 13,137, 27)( 12, 62, 58,129,133, 82,116, 53, 46,
139,131,140, 50, 77)( 15,134,150, 42, 72,144, 61, 52, 63, 83, 96,
25,118,135)( 19, 57)( 21, 54, 38,146,155, 45,154, 81, 26,105,151,
122, 55,115)( 23, 85,120, 93,145,108, 68, 75,125,156, 97,106, 40, 37
) ];
autGroups[13]:=
[ ( 1, 34, 33)( 2, 6, 11)( 3, 22, 18)( 4, 20, 53)( 5, 59, 52)
( 7, 62, 81)( 8, 70, 89)( 9, 93, 55)( 10, 13, 36)( 12, 75,111)
( 14,106, 61)( 15, 91, 83)( 16, 64, 29)( 17, 39, 90)( 19,119, 95)
( 21, 72,114)( 23,100,134)( 24,137, 35)( 25,117,131)( 26, 57, 40)
( 27, 44,136)( 28, 84, 47)( 30, 96, 48)( 31, 76, 77)( 32, 49, 68)
( 37, 42, 88)( 38,139,145)( 41,126,103)( 43,146, 63)( 45, 80, 86)
( 46, 97, 58)( 50,109,108)( 51, 82,104)( 54,129, 79)( 56,122, 85)
( 60,130,153)( 65,124,112)( 66,149,116)( 67,115, 73)( 69,152,121)
( 71,135,144)( 74,102,147)( 78,132, 98)( 87,128,107)( 92,101,133)
( 94,123,141)( 99,142,143)(105,156,138)(110,113,127)(118,125,151)
(120,150,155)(140,154,148), ( 1,151)( 2,146)( 3,133)( 4,156)
( 5,144)( 6,114)( 7,154)( 8,128)( 9, 79)( 10,152)( 11,137)
( 12,142)( 13, 97)( 14, 86)( 15,155)( 16,110)( 17,149)( 18,119)
( 19,121)( 20, 57)( 21,113)( 22, 89)( 23,150)( 24,131)( 25,148)
( 26,153)( 27,109)( 28, 95)( 29,129)( 30, 41)( 32,117)( 33, 59)
( 34,111)( 35, 76)( 36,136)( 37,102)( 38,140)( 40,126)( 42,141)
( 43,116)( 44, 83)( 45,143)( 46,132)( 48,135)( 49, 67)( 50, 87)
( 51,139)( 52, 93)( 53,106)( 54, 63)( 55, 84)( 56, 99)( 60,105)
( 61, 64)( 62, 88)( 65,123)( 66,120)( 68,147)( 69,138)( 70, 81)
( 71,118)( 72,145)( 73,122)( 74, 78)( 75,134)( 85,101)( 90,115)
( 94,130)( 96,103)( 98,125)(100,112)(108,127) ];
autGroups[14]:=
[ ( 1, 77, 78)( 2, 28, 98)( 3,114, 55)( 4, 54, 65)( 5, 84, 29)
( 6, 85,134)( 7, 51,111)( 8,115,106)( 9,124, 18)( 10, 19, 37)
( 11, 47,130)( 12, 32, 43)( 13,132,109)( 14,117, 86)( 15,133, 62)
( 16,145, 52)( 17, 69, 23)( 20, 45,116)( 21, 81, 76)( 22,118,143)
( 24, 40, 48)( 25, 83, 91)( 26, 90, 94)( 27,148, 87)( 30, 95,139)
( 31,147, 33)( 34, 68,153)( 35,129,120)( 36,125, 75)( 38, 73,137)
( 39, 57, 71)( 41,144, 63)( 42,123, 96)( 44,101,119)( 46,122, 60)
( 49, 61,100)( 50,151, 89)( 53, 80, 72)( 56,135,121)( 58,126, 70)
( 59,136,146)( 64,149, 97)( 66,128,104)( 67,131, 92)( 74,154,105)
( 79,110,141)( 82,113,127)( 88,150,112)( 93,156,142)( 99,140,152)
(102,107,138)(103,108,155),
( 1,152,139, 9, 97,129, 80, 87, 74, 23,128,135)( 2,137,109, 28, 75,
81, 82,106,123, 37, 73,151)( 3,104,100, 47,105, 41, 60,120,110,
12,140,141)( 4,155, 52, 19,143,115,113, 86, 36, 65, 83,145)
( 5,142,148, 31, 63, 64, 94, 49, 95, 7,156,121)( 6, 91, 71, 85,
42, 67,112, 76,138, 40,108,102)( 8, 99,154, 16, 35, 66,125, 30,
27, 38,149, 56)( 10,122, 55, 54,130, 32,127, 29, 90, 98, 51,147)
( 11,111,116,114, 26,126, 33, 43,153, 84, 46,119)( 13, 61, 25,118,
79, 14,103,144, 50, 21, 93, 96)( 15,136, 89, 24,146,117, 88, 92,
22, 62, 39,132)( 17,150, 18, 69,134, 77, 72, 48, 53, 78,133,124)
( 20, 57, 45, 68,107, 44, 70,131,101, 58, 59, 34) ];
autGroups[15]:=
[ ( 1,46,28, 9,15,49,53,18,45)( 2,37,17,56,55, 8,10,41,36)( 3,50,48,22,44,
27,13,16,23)( 4,12,40, 6,35,34,38,47,32)( 5,43,54,39,14,26,19,52,31)
( 7,24,21,11,25,42,29,30,51),
( 1,54,21,33,42,14,15,18,37,55,35,22,20,13,38,36,17,53)( 2, 5,32,45,29,
6, 3,47,24,49,40,19,56,16,43,51,26,48)( 4, 7,11,28,25,30,12,41,46,
52,50,44,10,27,23,31, 9, 8)(34,39) ];
autGroups[16]:=
[ ( 2, 3, 5, 8,11,14,17,20,19,16,13,10, 7, 4)( 6, 9)(12,15)(18,21),
( 1, 2, 3)( 4, 6, 5)( 7, 8, 9)(10,12,11)(13,14,15)(16,18,17)(19,20,21),
( 2, 3)( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20) ];
autGroups[17]:=
[ ( 2, 3, 5, 8,14,12, 7, 4)( 6, 9,15,24,36,26,16,10)(11,17,27,40,56,41,28,18
)(13,20,30,43,60,45,31,21)(19,22,32,46,65,59,42,29)(23,33,25,37,51,
67,47,34)(35,48,68,54,39,53,69,49)(38,50,70,62,44,61,72,52)
(55,73,81,63,80,79,83,74)(57,75,82,64,78,58,77,76)(66,84,88,89,86,71,
87,85), ( 1, 2, 3)( 4, 6, 5)( 7,11, 9)( 8,10,13)(12,19,17)(14,21,22)
(15,18,23)(16,25,20)(24,34,35)(26,38,37)(27,29,39)(28,30,33)
(31,44,32)(36,49,50)(40,54,55)(41,57,43)(42,58,53)(45,63,61)
(46,62,64)(47,66,48)(51,52,71)(56,74,75)(59,79,77)(60,76,80)
(65,82,83)(67,86,84)(68,85,73)(69,78,70)(72,81,87)(88,89,90),
( 2, 3)( 4, 5)( 7, 8)( 9,10)(11,13)(12,14)(15,16)(17,21)(18,20)(19,22)
(23,25)(24,26)(27,31)(28,30)(29,32)(34,37)(35,38)(39,44)(40,45)
(41,43)(42,46)(47,51)(48,52)(49,50)(53,62)(54,61)(55,63)(56,60)
(58,64)(59,65)(66,71)(68,72)(69,70)(73,81)(74,80)(75,76)(77,82)
(79,83)(84,86)(85,87)(88,89) ];
autGroups[18]:=
[ ( 1,35,54,87,86,41,59,11,68,90,38,62)( 2,57,28,91,81, 8,43,63,95,84,60,37)
( 3,13,44,78,89,24,45,39,94,92,33, 9)( 4,83,16,55,72,29,71,31,76,49,
18,79)( 5,22,23,53,36,70,64,19,85,50,74,46)( 6,27,61,69,75,14,77,80,
51,65,20,17)( 7,96,56,30,26,67,34,42,47,93,10,48)(12,88,82,58,66,73,
21,25,32,52,40,15),
( 1,46,73,47,69,45,57,52)( 2,62,50,18,89,39,83,61)( 3, 9,20,60,70,77,
35,22)( 4,81,80,76,78,19,48,90)( 5,33,41,66,88,43,13,17)
( 6,37,32,38,24,85,96,12)( 7,40,64,68,91,14,25,93)( 8,65,67,26,23,59,
27,74)(10,75,94,55,36,11,79,28)(15,92,29,86,63,71,44,21)
(16,56,82,95,87,58,42,49)(30,84,31,72,54,34,53,51) ];
autGroups[19]:=
[ ( 2, 3, 5, 8,11,14,17,20,23,22,19,16,13,10, 7, 4)( 6, 9)(12,15)(18,21),
( 1, 2, 3)( 4, 6, 5)( 7, 8, 9)(10,12,11)(13,14,15)(16,18,17)(19,20,21)
(22,24,23), ( 2, 3)( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20)(22,23) ];
autGroups[20]:=
[ ( 2, 3, 5, 8, 14, 12, 7, 4)( 6, 9, 15, 24, 36, 26, 16, 10)
( 11, 17, 27, 41, 57, 43, 28, 18)( 13, 20, 30, 46, 66, 48, 31, 21)
( 19, 22, 32, 49, 71, 62, 44, 29)( 23, 33, 50, 53, 38, 25, 37, 34)
( 35, 39, 52, 74, 92, 91, 73, 51)( 40, 54, 76, 87, 68, 47, 67, 55)
( 42, 58, 79, 84, 64, 45, 63, 59)( 56, 69, 86, 98,112,106, 93, 77)
( 60, 78, 94,107, 99, 88, 70, 80)( 61, 81, 95,109, 97, 85, 65, 82)
( 72, 75)( 83, 89,100,114,125,122,110, 96)( 90,101,115,108,121,113,
116,102)(103,104,118,105,119,123,111,117)(120,124),
( 1, 2, 3)( 4, 6, 5)( 7, 11, 9)( 8, 10, 13)( 12, 19, 17)
( 14, 21, 22)( 15, 18, 23)( 16, 25, 20)( 24, 34, 35)( 26, 39, 37)
( 27, 29, 40)( 28, 42, 33)( 30, 38, 45)( 31, 47, 32)( 36, 51, 52)
( 41, 55, 56)( 43, 60, 58)( 44, 61, 54)( 46, 64, 65)( 48, 69, 67)
( 49, 68, 70)( 50, 59, 72)( 53, 75, 63)( 57, 77, 78)( 62, 83, 81)
( 66, 85, 86)( 71, 88, 89)( 73, 90, 74)( 76, 82, 84)( 79, 80, 87)
( 91,103,101)( 92,102,104)( 93,105, 94)( 95, 96,108)( 97,111, 98)
( 99,113,100)(106,120,119)(107,118,116)(109,115,117)(110,114,121)
(112,123,124)(122,126,125), ( 2, 3)( 4, 5)( 7, 8)( 9, 10)
( 11, 13)( 12, 14)( 15, 16)( 17, 21)( 18, 20)( 19, 22)( 23, 25)
( 24, 26)( 27, 31)( 28, 30)( 29, 32)( 33, 38)( 34, 37)( 35, 39)
( 40, 47)( 41, 48)( 42, 45)( 43, 46)( 44, 49)( 50, 53)( 51, 52)
( 54, 68)( 55, 67)( 56, 69)( 57, 66)( 58, 64)( 59, 63)( 60, 65)
( 61, 70)( 62, 71)( 72, 75)( 73, 74)( 76, 87)( 77, 86)( 78, 85)
( 79, 84)( 80, 82)( 81, 88)( 83, 89)( 91, 92)( 93, 98)( 94, 97)
( 95, 99)( 96,100)(101,102)(103,104)(105,111)(106,112)(107,109)
(108,113)(110,114)(115,116)(117,118)(119,123)(120,124)(122,125) ];
autGroups[21]:=
[ ( 1, 36)( 2, 54)( 3, 53)( 4,106)( 5,103)( 6,121)( 7, 61)( 8, 70)
( 9, 87)( 10, 95)( 11, 88)( 12, 14)( 13, 94)( 15, 63)( 16, 67)
( 17, 21)( 18, 50)( 19, 22)( 20, 56)( 23, 76)( 24, 66)( 25, 84)
( 26, 75)( 27,107)( 28, 97)( 29,109)( 30, 91)( 31,101)( 32,102)
( 33, 96)( 34, 90)( 35, 92)( 37, 98)( 38, 86)( 39, 99)( 40, 85)
( 41, 58)( 42,117)( 43, 46)( 44, 60)( 45,110)( 47, 77)( 48, 72)
( 49, 73)( 51,113)( 52,100)( 55,115)( 57,108)( 59, 65)( 62, 68)
( 64, 69)( 71, 74)( 78, 89)( 79,125)( 80,116)( 81,112)( 82, 93)
( 83,124)(104,126)(105,111)(114,118)(119,122)(120,123),
( 1, 59, 87,122, 32, 50, 24, 99, 16, 38, 19,101,111, 57)
( 2, 34, 98, 55, 5, 30, 41,124, 52,108, 39,116, 31, 18)
( 3,104, 74,110, 20, 93, 83, 66, 51, 63, 11,105, 90, 82)
( 4, 10, 21, 68, 27, 15, 8, 49, 96,120, 64,109, 80, 29)
( 6, 37,126, 23, 9,118, 45, 58, 78,115, 73, 47, 62, 91)
( 7, 72, 53,113, 81, 86, 14, 88, 56, 79, 92,106, 77, 69)
( 12,117,103, 42,112, 95, 46, 22, 28, 60, 94, 67, 85,123)
( 13, 71, 97, 76, 33, 43,119, 70, 25,107, 65, 40, 17,114)
( 26,125, 36, 84,102, 48, 75, 54, 89, 35, 44, 61,121,100) ];
autGroups[22]:=
[ ( 2, 3, 5, 8,14,23,20,12, 7, 4)( 6, 9,15,24,35,50,36,25,16,10)
(11,17,26,38,55,43,30,21,13,18)(19,27,39,45,32,22,31,44,40,28)
(29,33,46,61,59,69,68,54,57,41)(34,47,62,53,37,52,42,58,63,48)
(49,64,60,56,67,51,66,71,70,65),
( 1, 2, 3)( 4, 6, 5)( 7,11, 9)( 8,10,13)(12,19,17)(14,21,22)(15,18,16)
(20,29,27)(23,32,33)(24,25,34)(26,28,37)(30,42,31)(35,48,49)
(36,51,47)(38,53,54)(39,41,56)(40,44,52)(43,59,58)(45,60,46)
(50,65,66)(55,68,69)(57,62,67)(61,64,63)(70,72,71),
( 2, 3)( 4, 5)( 7, 8)( 9,10)(11,13)(12,14)(15,16)(17,21)(19,22)(20,23)
(24,25)(26,30)(27,32)(28,31)(29,33)(35,36)(37,42)(38,43)(39,45)
(40,44)(41,46)(47,48)(49,51)(53,58)(54,59)(56,60)(57,61)(62,63)
(64,67)(65,66)(68,69)(70,71) ];
autGroups[23]:=
[ ( 2, 3, 5, 8,14,24,37,32,20,12, 7, 4)( 6, 9,15,26,16,10)(11,17,28,18)
(13,21,33,22)(19,29,30)(23,34,35)(25,38,31,42,44,36,41,27,40,47,46,39
)(43,45), ( 1, 2, 3)( 4, 6, 5)( 7,11, 9)( 8,10,13)(12,19,17)
(14,22,23)(15,18,25)(16,27,21)(20,31,29)(24,35,36)(26,39,40)
(28,30,38)(32,43,42)(33,41,34)(37,44,45)(46,48,47),
( 2, 3)( 4, 5)( 7, 8)( 9,10)(11,13)(12,14)(15,16)(17,22)(18,21)(19,23)
(20,24)(25,27)(28,33)(29,35)(30,34)(31,36)(32,37)(38,41)(39,40)
(42,44)(43,45)(46,47) ];
autGroups[24]:=
[ ( 1,32,15,28,23)( 2,11,61,25,13,24,18,44,68,22)( 3,20,63,34,41,14, 4,45,
29,58)( 5,73,38,12,39, 8,51,59, 7,71)( 6,60,50,52,36,42,10,19,48,37)
( 9,54,74,65,16,26,49,75,31,46)(17,21,67,53,64,30,35,55,72,66)
(27,69,47,56,70,43,57,62,40,33),
( 1,63,27,75,12,18,48,55,64,52,22, 5,74,56,58)( 2,15,62,57,28,24,39, 6,
59,17,10,29,70,16,25,14, 9,53,72,46, 4,61,26,33,34,42,21,51,60,71)
( 3,38,31,66, 7,50,30,47,65,43,40,49,69,35,37, 8,67,54,73,20,32,11,
45,19,44,68,36,41,13,23) ];
--> --------------------
--> maximum size reached
--> --------------------
[ Dauer der Verarbeitung: 0.14 Sekunden
(vorverarbeitet)
]
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