#%Format: latex
#%This file can be pasted directly to GAP
\Read("E8.txt");
#\table
#=E8+A4+A3+2A2\\\1&&E8-3333&(1,0)&\tref{arg.E8+A4+A3+2A2}%
 \size(5,4,3);#\cr
#E8+A11&&E8-9111=\-1&(0,1)&\tref{lem.E8.loop}%
 \size(\0,\0,1);#\cr
#E8+A9+A2&\same1 &E8-9111=2&(1,0)&\tref{lem.E8.loop}%
 \size(3,\0,\0);#\cr
#E8+A10+A1&\same2 &E8-9111=3&(1,0)&\tref{lem.E8.loop}\cr
#E8+A7+2A2&&E8-6321=1&(1,0)&\\
 \size(8,3,3);#\note2\cr
#E8+A6+A3+A2&&E8-6321=2&(1,0)&\\
 \size(4,7,3);#\note2\cr
#E8+A5+A4+A2&\same3 &E8-6321=3&(1,0)&\\
 \size(5,3,6);#\note2\cr
#E8+A6+A4+A1&\same4 &E8-6321=\-4&(0,1)&\\
 \size(5,7,2);#\note2\cr
#E8+A8+A2+A1&\same5 &E8-6321=\-5&(0,1)&\tref{lem.E8.loop}%
 \size(\0,\0,1);#\cr
#E8+A6+2A2+A1&&E8-6321=6&(1,0)&\tref{lem.E8.loop}%
 \size(3,\0,\0);#\cr
#E8+A6+A5&&E8-5511=\-1&(0,1)&\\
 \size(7,\0,\0);#\note2\cr
#E8+A7+A4&&E8-5511=\-2&(0,1)&\tref{lem.E8.loop}%
 \size(\0,\0,1);#\cr
#E8+A5+A4+A2&\same3 &E8-5511=3&(1,0)&\tref{lem.E8.loop}%
 \size(3,\0,\0);#\cr
#E8+A6+A4+A1&\same4 &E8-5511=4&(1,0)&\tref{lem.E8.loop}\cr
#E8+A8+A3&&E8-8211=1&(1,0)&\\
 \size(4,9,9);#\note2\cr
#E8+A10+A1&\same2 &E8-8211=\-2&(0,1)&\tref{lem.E8.loop}%
 \size(\0,\0,1);#\cr
#E8+A8+A2+A1&\same5 &E8-8211=3&(1,0)&\tref{lem.E8.loop}%
 \size(3,\0,\0);#\cr
#=E8+D11&&E8-411=1&(1,0)&\tref{lem.E8.loop}%
 \size(\0,\0,1);#\cr
#E8+D5+A6&&E8-411=\-1&(0,1)&\tref{lem.E8.loop}%
 \size(\0,\0,1);#\cr
#E8+D9+A2&&E8-411=2&(1,0)&\tref{lem.E8.loop}%
 \size(3,\0,\0);#\cr
#E8+D7+A4&&E8-411=2&(1,0)&\\
 \size(\0,5,5);#\note2\cr
#=E8+D5+A4+A2&&E8-411=2&(1,0)&\tref{lem.E8.loop}%
 \size(3,\0,\0);#\cr
#E8+E6+A5&&E8-31=\-1&(0,1)&\tref{lem.E8.loop}%
 \size(\0,\0,1);#\cr
#E8+E6+A3+A2&&E8-31=2&(1,0)&\tref{lem.E8.loop}%
 \size(3,\0,\0);#\cr
#E8+E6+A4+A1&&E8-31=3&(1,0)&\tref{lem.E8.loop}\cr
#E8+E7+A4&&E8-21=\-1&(0,1)&\tref{lem.E8.loop}%
 \size(\0,\0,1);#\cr
#E8+E7+2A2&&E8-21=2&(1,0)&\tref{lem.E8.loop}%
 \size(3,\0,\0);#\cr
#2E8+A2+A1&&E8-11&(1,0)&\tref{lem.E8.loop}\cr
#2E8+A3&&E8-E8&(1,0)&\tref{lem.E8.loop}%
 \size(\0,\0,1);#\cr
#=E8+E6+D5&&E8-E6&(1,0)&\tref{arg.E8+E6+D5}\cr
#\endtable
#\endinput

## Further processing for E8+A4+A3+2A2
sh := size(5,4,3);
# Sizes are equal, hence the last two relations can be omitted
sh = size(5,0,0);
StructureDescription(h);
c := Centralizer(g, h);
Size(Intersection(c, h));
StructureDescription(c);

## Further processing for E8+E6+D5
Size(DS(Union(fixed, E6([]))));
