#m12b.g

M12 := MathieuGroup( 12 );
M12.generators;
 h1:=(1,12)(2,11)(3,10)(4,9)(5,8)(6,7);
h2:=(2,3,5,9,8,10,6,11,4,7,12);
IsSimple(H);
Size(H);
F2 := FreeGroup( "a", "b");
words := [ F2.1, F2.2 ];
P := PresentationViaCosetTable( H, F2, words );
G := FpGroupPresentation( P );
G.relators;
SimplifyPresentation( P );