(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 65 66 67)

(2 38 30)(3 8 59)(4 45 21)(5 15 50)(6 52 12)(7 22 41)(9 29 32)(10 66 61)(11 36 23)(13 43 14)(16 20 34)(17 57 63)(18 27 25)(19 64 54)(24 48 65)(26 55 56)(28 62 47)(31 39 67)(33 46 58)(35 53 49)(37 60 40)(42 44 51)

G:=sub<Sym(67)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67), (2,38,30)(3,8,59)(4,45,21)(5,15,50)(6,52,12)(7,22,41)(9,29,32)(10,66,61)(11,36,23)(13,43,14)(16,20,34)(17,57,63)(18,27,25)(19,64,54)(24,48,65)(26,55,56)(28,62,47)(31,39,67)(33,46,58)(35,53,49)(37,60,40)(42,44,51)>;

G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67), (2,38,30)(3,8,59)(4,45,21)(5,15,50)(6,52,12)(7,22,41)(9,29,32)(10,66,61)(11,36,23)(13,43,14)(16,20,34)(17,57,63)(18,27,25)(19,64,54)(24,48,65)(26,55,56)(28,62,47)(31,39,67)(33,46,58)(35,53,49)(37,60,40)(42,44,51) );

G=PermutationGroup([[(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67)], [(2,38,30),(3,8,59),(4,45,21),(5,15,50),(6,52,12),(7,22,41),(9,29,32),(10,66,61),(11,36,23),(13,43,14),(16,20,34),(17,57,63),(18,27,25),(19,64,54),(24,48,65),(26,55,56),(28,62,47),(31,39,67),(33,46,58),(35,53,49),(37,60,40),(42,44,51)]])

G:=sub<GL(3,GF(1609))| [0,0,1,1,0,16,0,1,447],[1,1462,629,0,597,1180,0,1256,1011] >;