#%Format: latex
#%This file can be pasted directly to GAP
\Read("E7.txt");
#\table
#=E7+2A4+2A2\\\1&&E7-3333&(1,0)&\tref{arg.E7+2A4+2A2}%
 \size(5,5,3);#\cr
#E7+A12&&E7-9111=1&(0,1)&\\
 \size(13,\0,1);#\note2\cr
#=E7+A10+A2&&E7-9111=2&(2,0)&\\ %\tref{arg.E7.loop}%
 \size(11,3);
 \size(3,11);#\note2\cr
#E7+2A6&&E7-5511=\-1&(0,1)&\\
 \size(7,7,\0,1);#\note2\cr
#E7+A8+A4&&E7-5511=2&(0,1)&\\
 \size(9,\0,1);#\note2\cr
#=E7+A6+A4+A2&&E7-5511=3&(2,0)&\\ %\tref{arg.E7.loop}%
 \size(7,3);
 \size(3,7);#\note2\cr
#\endtable
#\endinput

## Further processing for E7+2A4+2A2
sh := size(5,5,3);
# Sizes are equal, hence the last relation can be omitted
sh = size(5,5);
NumberPerfectGroups(sh);
PerfectGroup(sh);
c := Centralizer(g, h);
Size(c);
AbelianInvariants(c);
Size(Intersection(c, h));
