## Point graph of GQ(3,5) and the hexacode on 64 vertices from 2^6:3.Sym(6) with rank 3


GQ35:=EdgeOrbitsGraph(Group(
[ ( 2, 8, 5, 3)( 4, 7)( 9,49,41,17)(10,56,45,19)(11,50,48,21)(12,55,44,23)
    (13,51,42,24)(14,54,46,22)(15,52,47,20)(16,53,43,18)(25,57)(26,64,29,59)
    (27,58,32,61)(28,63)(30,62)(31,60)(34,40,37,35)(36,39), 
  ( 2, 6,50,18)( 3,45,39, 9)( 4,42,24,26)( 5,53,33,17)( 7,25)( 8,30,56,10)
    (11,47)(12,44,60,64)(13,55)(14,52,62,40)(15,27,43,63)(16,32,28,48)(19,41)
    (20,46,36,58)(21,49)(22,54,38,34)(23,29,51,57)(35,61), 
  ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)
    (21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)
    (41,42)(43,44)(45,46)(47,48)(49,50)(51,52)(53,54)(55,56)(57,58)(59,60)
    (61,62)(63,64) ]), [ [1,4] ]);