(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)

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

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

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

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

G:=sub<GL(3,GF(13))| [11,9,4,9,9,2,0,1,0],[1,0,0,0,0,1,4,12,12] >;