THE REV. T. P. KIRKMAN ON NON-MODULAR GROUPS. 219 



Substitutions of the Second Order. 



A 35162487 

 B 38176542 

 C 34127856 



ly 87563421 



E 21768435 

 F 58431762 



a 18367452 



b 37148625 

 c 32154768 

 d 36185274 

 e 42615387 

 / 65432178 

 g 21875643 



G 78654312 

 H 63287154 

 I 46817253 

 J 45712836 

 K 85672341 



h 83246971 

 i 54721638 

 J 72543816 

 k 52861473 

 I 73265418 

 m 48513672 

 n 68745132 



L 64523187 

 M 21436587 

 N 86754231 

 P 43218765 

 Q 53271846 



p 21647358 

 q 82437651 

 r 15842763 

 * 75382614 

 t 13254687 

 u 56341287 

 y 12786534 



R 21583764 

 S 74826513 

 T 57681324 

 U 67854123 

 V 76438215 



w 47316528 

 X 16573248 

 y 62378145 

 z 21354876 

 « 17435826 

 /3 84325761 

 y 14628375 



Substitutions of the Eighth Order, 



flL=6 = 

 tB = K = 



a;M. = v 

 «A=^= 

 aP = 7r- 

 «6E=p = 



yF=r= 



rB = (o- 

 rT = «i 



rE=/3i 



73851264, 

 46783125, 

 =27458361, 

 =31867524, 

 =86527314, 

 =78462531, 

 =57164832, 

 = 53126784, 

 = 61752384, 

 =45187362, 

 = 34716285, 

 =71286345, 

 = 65173824, 

 = 85261734, 

 = 57836241, 

 =43657821, 

 = 76152843, 

 =64871352, 

 = 83167245, 

 = 26731854, 

 = 51673482, 



S^ =24576831, 

 e^ =54632817, 

 773=63812547, 

 93=48671235, 

 i3 =25138746, 

 rS =47521863, 

 \3 = 6i428753, 

 ^3 = 75618423, 

 ^3 = 73416852, 

 43 =26853417, 

 ^^ = 83574162, 

 p3 =84762153, 

 (t3;=4i856732, 

 73=68134257, 

 u3 =28714563, 

 ^3 = 78123465, 



x^= 53468127, 



i//3= 8541 3267, 

 '''^^ 78536124, 



«? =84156327, 

 /3? = 6372481 5, 



^5 =81723546, 



e5 =75421386, 

 J75'=45276i83, 

 95 = 56718342, 



t5 =31472865, 

 k5 = 54813726, 



X5 = 24837i65, 

 )u5=478623i5, 

 1/8 = 48237516, 

 ^5=71564283, 

 7r5 = 6825374i, 

 p5 =65827431, 

 (T"'' =28714563, 

 75 = 36457182, 

 w5 =41263857, 

 0^=34568712, 

 X5=6723i485, 

 ^//5 =46 5 32781, 

 0)5 = 67483512, 

 af = 37624581, 

 185 = 74258 136, 



^7=56284713, 

 6^ = 67518234, 

 »;7 = 81 634725, 

 07=27186453, 

 t? =74683251, 



k7 =85736412, 



X7 = 38751426, 

 Ai7= 34281567, 

 ^7 = 25684137, 

 47 = 38612754, 

 777=46128537, 

 p7 = 236785i4, 

 <r7 = 37582146, 

 77=53782461, 

 y7 = 86471523, 

 ^7 = 87214356, 



x^= 35874216 



^7=58627143, 

 0)7 = 36278451, 

 aj = 51487236, 

 /3t = 28561 347. 



