#%Format: latex
#%This file can be pasted directly to GAP
\Read("E6.txt");
#\table
#=(E6+2A5)+A3.1\\\2\label{E6.r.first}&\same14 &E8-6321-r=1&(1,0)&%
 #\tref{arg.E6.loop.tt}%
 \group2l(4,6,6);#%
 #% Not isomorphic to any braid group:
 \qsize(g.1^2);#%> 24
 #% Irreducible perturbations of torus type:
 \group1l(1,6,6);#%
 \simplify(g.1/g.2);#%
 \group1l(4,6,3);#%
 \simplify(g.1/g.2);#%
 #% Perturbations not of torus type:
 \size2l(4,2,6);#%
 \size2l(4,6,2);#\cr%
#E6+A7+A5+A1&\same15 &E8-6321-r=\-2&(0,1)&\tref{arg.E6.loop}%
 \size2l(\0,\0,2);#\cr%
#=E6+A7+A3+A2+A1.1\\\1&\same16 &E8-6321-r=3&(1,0)&%
 #\tref{arg.E6.loop.na}\iref{item.E6+A7+A3+A2+A1.1}%
 \size2l(8,4,\0,3);#%
 \StructureDescription(h);#%> SL(2,7)
 \Size(Centralizer(g, h));#%
 \Size(Intersection(Centralizer(g, h), h));#\cr%
#E6+A6+A5+2A1&\same17 &E8-4422-r=1&(1,0)&\tref{arg.E6.loop}%
 \size2l(\0,\0,2);#\cr%
#=E6+A5+A4+A3+A1.1\\\1&\same18 &E8-4422-r=2&(1,0)&%
 #\tref{arg.E6.loop.na}\iref{item.E6+A5+A4+A3+A1.1}%
 \size2l(6,5,4);#%
 \StructureDescription(h);#%> SL(2,5)
 \Size(Centralizer(g, h));#%
 \Size(Intersection(Centralizer(g, h), h));#\cr%
#E6+A6+2A3+A1&&E8-4422-r=3&(1,0)&\tref{arg.E6.loop}%
 \size2l(4,7,4);#%
 #\cr%
#E6+A9+A4&\same10 &E8-8211-r=1&(1,0)&\tref{arg.E6.loop}%
 \size2l(\0,\0,\0,1);#\cr%
#E6+A9+A3+A1&\same19 &E8-8211-r=2&(1,0)&\tref{arg.E6.loop}%
 \size2l(10,4,\0,2);#\cr%
#E6+D9+A3+A1&&E8-222-r&(1,0)&\tref{arg.E6.loop}%
 \size2l(\0,\0,2);#\cr%
#E6+D8+A4+A1&&E8-222-r&(1,0)&\tref{arg.E6.loop}%
 \size2l(\0,\0,2);#\cr%
#E6+D6+A4+A3&&E8-222-r&(1,0)&\tref{arg.E6.loop}%
 \size2l(4,5);#\cr%
#=E6+D5+A4+A3+A1&&E8-222-r&(1,0)&\tref{arg.E6+D5+A8}%
 \Size(DS(AA(c2l, [4,5,2]), [kappa]));#\cr%
#E6+D10+A3&&E8-411-r&(1,0)&\tref{arg.E6.loop}%
 \size2l(\0,\0,\0,1);#\cr%
#E6+D8+A5&&E8-411-r&(1,0)&\tref{arg.E6.loop}%
 \size2l(\0,\0,\0,1);#\cr%
#=E6+D5+A5+A3.1\\\1&\same20 &E8-411-r&(1,0)&%
 #\tref{arg.E6.loop.na}\iref{item.E6+D5+A5+A3.1}%
 \size2l(6,4);#%
 \StructureDescription(h);#%> (C3 x C3) : C3
 \Size(Centralizer(g, h));#%
 \Size(Intersection(Centralizer(g, h), h));#\cr%
#=E6+D5+A5+A3.2\\\1&\same20 &E8-411-r&(1,0)&\tref{arg.E6+D5+A8}%
 \Size(DS(AA(c2l, [6,4,\0,1]), [kappa]));#%
 \StructureDescription(h);#%> (C3 x C3) : C3
 \Size(Centralizer(g, h));#%
 \Size(Intersection(Centralizer(g, h), h));#\cr%
#E6+D7+D6&&E8-00-r&(1,0)&\tref{arg.E6.loop}%
 \Size(DS(fixed, loop2, D(x, 2), D(x^2, 3)));#\cr%
#=E6+D7+D5+A1&&E8-00-r&(1,0)&\tref{arg.E6+D5+A8}%
 \Size(DS(AA(c2l, [2]), D(x^2, 3), [kappa]));#\cr%
#=E6+D6+D5+A2\\\label{E6.r.last}&&E8-00-r&(1,0)&\tref{arg.E6+D5+A8}%
 \Size(DS(AA(c2l, [0,3]), D(x, 2), [kappa]));#\cr%
#\midrule
#=(E6+A5+2A2)+A3+A1\\\2&&[fig.hex.r]h263436&(1,0)&\tref{arg.E6.hex}%
 \group0h(6,3,4,3,\0,2);#%
 #% This one is considered as a perturbation of (2E6+2A2)+A3
 \group0h(3,3,4,3,\0,2);#%
 #% Other irreducible perturbations of torus type:
 \group0h(6,3,1,3,\0,2);#%
 \simplify(g.1/g.2);#\cr%
#=E6+A4+2A3+A2+A1\\\4&&[fig.hex.r]h254345&(1,0)&\tref{arg.E6.hex}%
 \group0h(5,4,3,4,\0,2);#%
 #% Irreducible perturbations:
 \Size(group0h(5,1,3,4,\0,2));#%
 \Size(group0h(5,4,3,4,\0,1));#\cr%
#E6+A7+A3+3A1\\\1&&[fig.hex.r]h282848&(1,0)&\tref{arg.E6.3}%
 #%(2,8,2,\0,4,\0)
 #% Irreducible perturbations:
 \Size(group0h(1,1));#%
 \Size(group0h(1,2,\0,1));#\cr%
#E6+A5+2A3+2A1\\\1&&[fig.hex.r]h246464&(1,0)&\tref{arg.E6.3}%
 #%(2,4,6,4,\0,\0)
 #% Irreducible perturbations:
 \Size(group0h(1,1));#%
 \Size(group0h(1,4,4,1));#\cr%
#(E6+2A5)+3A1\\\2&&[fig.hex.r]h266266&(1,0)&\tref{arg.E6.3}%
 #%(2,6,6,2,\0,\0)
 #% This one is considered as a perturbation of (2E6+2A2)+A3
 \group0h(2,3,3,2);#%
 #% Other irreducible perturbations of torus type:
 \group0h(1,6,6,1);#%
 \simplify(g.1/g.2);#\cr%
#=E6+A9+A3+A1&\same19 &[fig.hex.r]h1010421010&(1,0)&%
 #\tref{arg.E6.2.monogon}%
 \Size(group2h(10,\0,4,2));#\cr%
#E6+A11+2A1&\same21 &[fig.hex.r]h1212212212&(1,0)&%
 #\tref{arg.E6.2.monogon}%
 \Size(group2h(12,\0,2,\0,2));#\cr%
#E6+A7+A5+A1&\same15 &[fig.hex.r]h882866&(0,1)&%
 #\tref{arg.E6.2.monogon}%
 \Size(group2h(8,\0,2,\0,6));#\cr%
#=(E6+A11)+2A1.2\\\2&\same21 &[fig.hex.r]h1212212122&(1,0)&%
 #\tref{arg.E6.2.monogon}%
 \group2h(12,\0,2,\0,\0,2);#%
 #% Irreducible perturbations of torus type
 \DS(AA(ch, [3,\0,2,\0,\0,2]), A((y*x^2)^2, 1));#%
 \simplify(g.1/g.2);#%
 #% Perturbations not of torus type
 \Size(\group2h(4,\0,2,\0,\0,2));#\cr%
#=(E6+2A5)+A3.2\\\2&\same14 &[fig.hex.r]h664664&(1,0)&%
 #\tref{arg.E6.2.monogon}%
 \group2h(6,\0,4,6);#%
 #% Irreducible perturbations of torus type
 \DS(AA(ch, [3,\0,4,6]), A((y*x^2)^2, 1));#%
 \simplify(g.1/g.2);#%
 #% Perturbations not of torus type
 \Size(\group2h(2,\0,4,6));#\cr%
#=E6+A5+A4+A3+A1.2\\\1&\same18 &[fig.hex.r]h654245&(1,0)&%
 \tref{arg.E6.1.monogon}\iref{item.E6+A5+A4+A3+A1.2}%
 \Size(group1h(6,5,4,2));#%
 \StructureDescription(h);#%> SL(2,5)
 \AbelianInvariants(g);#%
 \Size(Centralizer(g, h));#%
 \Size(Intersection(Centralizer(g, h), h));#%
 #% Irreducible perturbations:
 \Size(group0h(3,5,4,2));#%
 \Size(group0h(6,5,1,2));#\cr%
#E6+A6+A5+2A1&\same17 &[fig.hex.r]h672727&(1,0)&\tref{arg.E6.1.monogon}%
 \Size(group1h(6,7,2,\0,2));#\cr%
#E6+A7+A4+2A1&&[fig.hex.r]h852582&(1,0)&\tref{arg.E6.1.monogon}%
 \Size(group1h(8,5,2,\0,\0,2));#\cr%
#=E6+A7+A3+A2+A1.2\\\1&\same16 &[fig.hex.r]h838424&(1,0)&%
 \tref{arg.E6.1.monogon}\iref{item.E6+A7+A3+A2+A1.2}%
 \Size(group1h(8,3,\0,4,2));#%
 \StructureDescription(h);#%> SL(2,7)
 \AbelianInvariants(g);#%
 \Size(Centralizer(g, h));#%
 \Size(Intersection(Centralizer(g, h), h));#%
 #% Irreducible perturbations:
 \Size(group0h(1,3,\0,4,2));#%
 \Size(group0h(8,3,\0,4,1));#\cr%
#=E6+A9+A2+2A1\\\1&&[fig.hex.r]h103102102&(1,0)&%
 \tref{arg.E6.1.monogon}\iref{item.E6+A9+A2+2A1}%
 \group1h(10,3,\0,2,\0,2);#%
 \AbelianInvariants(h);#%>
 \group0h(10,3,\0,2,\0,2);#%
 \Size(DerivedSubgroup(qgroup(g.3^2)));#%> 60
 \Size(DerivedSubgroup(qgroup(g.3^3)));#%> 51840
 #% Irreducible perturbations:
 \Size(group0h(5,3,\0,2,\0,2));#\cr%
#=E6+D8+A3+2A1&&[fig.hex.r]h244244&(1,0)&\tref{arg.E6.3}%
 \Size(DS(AA(ch, [\0,4,2,\0,\0,2]), [kappa, G.1*(G.2*G.3)^3]));#\cr%
#E6+D6+2A3+A1\\\1&&[fig.hex.r]h244244&(1,0)&\tref{arg.E6.3}%
 \DS(AA(ch, [\0,4,4,2]), [kappa, G.1*(G.2*G.3)^2]);#%
 \AbelianInvariants(h);#\cr%
#E6+D10+3A1\\\1&&[fig.hex.r]h262626&(1,0)&\tref{arg.E6.3}%
 \DS(AA(ch, [\0,2,\0,2,\0,2]), [kappa, G.1*(G.2*G.3)^4]);#%
 \AbelianInvariants(h);#\cr%
#=E6+D6+A5+2A1&&[fig.hex.r]h262626&(1,0)&\tref{arg.E6.3}%
 \Size(DS(AA(ch, [\0,6,2,\0,2]), [kappa, G.1*(G.2*G.3)^2]));#\cr%
#\endtable
#\endinput
