(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 68 69 70 71 72 73 74 75 76 77 78 79)

(2 24 56)(3 47 32)(4 70 8)(5 14 63)(6 37 39)(7 60 15)(9 27 46)(10 50 22)(11 73 77)(12 17 53)(13 40 29)(16 30 36)(18 76 67)(19 20 43)(21 66 74)(23 33 26)(25 79 57)(28 69 64)(31 59 71)(34 49 78)(35 72 54)(38 62 61)(41 52 68)(42 75 44)(45 65 51)(48 55 58)

G:=sub<Sym(79)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79), (2,24,56)(3,47,32)(4,70,8)(5,14,63)(6,37,39)(7,60,15)(9,27,46)(10,50,22)(11,73,77)(12,17,53)(13,40,29)(16,30,36)(18,76,67)(19,20,43)(21,66,74)(23,33,26)(25,79,57)(28,69,64)(31,59,71)(34,49,78)(35,72,54)(38,62,61)(41,52,68)(42,75,44)(45,65,51)(48,55,58)>;

G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79), (2,24,56)(3,47,32)(4,70,8)(5,14,63)(6,37,39)(7,60,15)(9,27,46)(10,50,22)(11,73,77)(12,17,53)(13,40,29)(16,30,36)(18,76,67)(19,20,43)(21,66,74)(23,33,26)(25,79,57)(28,69,64)(31,59,71)(34,49,78)(35,72,54)(38,62,61)(41,52,68)(42,75,44)(45,65,51)(48,55,58) );

G=PermutationGroup([[(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79)], [(2,24,56),(3,47,32),(4,70,8),(5,14,63),(6,37,39),(7,60,15),(9,27,46),(10,50,22),(11,73,77),(12,17,53),(13,40,29),(16,30,36),(18,76,67),(19,20,43),(21,66,74),(23,33,26),(25,79,57),(28,69,64),(31,59,71),(34,49,78),(35,72,54),(38,62,61),(41,52,68),(42,75,44),(45,65,51),(48,55,58)]])

G:=sub<GL(3,GF(1423))| [0,0,1,1,0,490,0,1,104],[1,859,630,0,1374,1246,0,970,48] >;