order found ------------ 1 37 2 > 5000 3 0 4 45 5 1 6 2 7 0 8 2 9 1 > 1 Known Sociable Groups of order > 4 discovered until 1998-02-01: 1. p = 5 gcd = 2*2*2 Poulett (1918) 12496 = 2*2*2*2*11*71 14288 = 2*2*2*2*19*47 15472 = 2*2*2*2*967 14536 = 2*2*2*23*79 14264 = 2*2*2*1783 1. p = 28 gcd = 2 Poulett (1918) 14316 = 2*2*3*1193 19116 = 2*2*3*3*3*3*59 31704 = 2*2*2*3*1321 47616 = 2*2*2*2*2*2*2*2*2*3*31 83328 = 2*2*2*2*2*2*2*3*7*31 177792 = 2*2*2*2*2*2*2*3*463 295488 = 2*2*2*2*2*2*3*3*3*3*3*19 629072 = 2*2*2*2*39317 589786 = 2*294893 294896 = 2*2*2*2*7*2633 358336 = 2*2*2*2*2*2*11*509 418904 = 2*2*2*52363 366556 = 2*2*91639 274924 = 2*2*13*17*311 275444 = 2*2*13*5297 243760 = 2*2*2*2*5*11*277 376736 = 2*2*2*2*2*61*193 381028 = 2*2*95257 285778 = 2*43*3323 152990 = 2*5*15299 122410 = 2*5*12241 97946 = 2*48973 48976 = 2*2*2*2*3061 45946 = 2*22973 22976 = 2*2*2*2*2*2*359 22744 = 2*2*2*2843 19916 = 2*2*13*383 17716 = 2*2*43*103 1. p = 9 gcd = 2 A.F. (1989) 805984760 = 2*2*2*5*7*1579*1823 1268997640 = 2*2*2*5*17*61*30593 1803863720 = 2*2*2*5*103*367*1193 2308845400 = 2*2*2*5*5*11544227 3059220620 = 2*2*5*2347*65173 3367978564 = 2*2*841994641 2525983930 = 2*5*17*367*40487 2301481286 = 2*13*19*4658869 1611969514 = 2*805984757 1. p = 8 gcd = 2*2*2 A.F. (1989) 1095447416 = 2*2*2*7*313*62497 1259477224 = 2*2*2*43*3661271 1156962296 = 2*2*2*7*311*66431 1330251784 = 2*2*2*43*3867011 1221976136 = 2*2*2*41*1399*2663 1127671864 = 2*2*2*11*61*83*2531 1245926216 = 2*2*2*19*8196883 1213138984 = 2*2*2*67*2263319 2. p = 8 gcd = 2*2 A.F. (1989) 1276254780 = 2*2*3*5*1973*10781 2299401444 = 2*2*3*991*193357 3071310364 = 2*2*767827591 2303482780 = 2*2*5*67*211*8147 2629903076 = 2*2*23*131*218213 2209210588 = 2*2*13*13*17*192239 2223459332 = 2*2*131*4243243 1697298124 = 2*2*907*467833 1. p = 6 gcd = 3*3*7*7*13*19 Moews (1992) 21548919483 = 3*3*3*3*3*7*7*13*17*19*431 23625285957 = 3*3*3*3*3*7*7*13*19*29*277 24825443643 = 3*3*7*7*11*13*19*20719 26762383557 = 3*3*3*3*7*7*13*19*27299 25958284443 = 3*3*7*7*13*19*167*1427 23816997477 = 3*3*7*7*13*19*218651 2. p = 6 gcd = 2*2 Moews (1993) 90632826380 = 2*2*5*109*431*96461 101889891700 = 2*2*5*5*31*193*170299 127527369100 = 2*2*5*5*31*181*227281 159713440756 = 2*2*31*991*1299709 129092518924 = 2*2*31*109*9551089 106246338676 = 2*2*17*25411*61487