#m24b.g

h:=[];

h[1]:=();
h[2]:=(1,24)(2,13)(3,14)(4,15)(5,16)(6,17)(7,18)(8,19)*
(9,20)(10,21)(11,22)(12,23);
h[3]:=(2,3,4,5,6,7,8,9,10,11,12)*
(13,14,15,16,17,18,19,20,21,22,23);
h[4]:=(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23);
h[5]:=(24,21,20,13,19,5,23,3,18,16,6,9,22,14,4,2,17,8,15,12,7,11,10);
h[6]:=(2,3,4,5,6,7,8,9,10,11,12)*
(13,14,15,16,17,18,19,20,21,22,23)^-1;
h[7]:=(4,8,9,12,10)(7,6,3,5,11)(15,19,20,23,21)(18,17,14,16,22);
h[8]:=(1,2,3,4,5,6,7,8,9,10,11,12)(13,14,15,16,17,18,19,20,21,22,23,24);
h[9]:=(1,2,3,4,5,6,7,8,9,10,11,12)*
(13,14,15,16,17,18,19,20,21,22,23,24)^-1;

#H:=Group(h[1],h[2],h[6],h[7],h[8]);

M23:=Group(h[5],h[7]);

F2:= FreeGroup( "a", "b");
words := [ F2.1, F2.2 ];
P := PresentationViaCosetTable(M23,F2,words);
SimplifyPresentation(P);
M24:=Group(h[1],h[2],h[5],h[7]);