On Recognition of the Sporadic Simple Groups <span class='InlineEquation' id='IEq1'>( HS )span>,<span class='InlineEquation' id='IEq2'>( J_{3} )span>,<span class='InlineEquation' id='IEq3'>( Suz )span>,<span class='InlineEquation' id='IEq4'>( O^{prime}N )span>,<span class='InlineEquation' id='IEq5'>( Ly )span>,<span class=