46 The Rev. Thos. P. Kirk man on 



S = oa/3/3yy. 



O d =(436521), G M =(254631), G M = (316245), G 4<l = (462315) 

 G e i= 651234, G 2ol = 614523, G 3el = 235164, G 4el = 541362 

 G t2 = 561243, G 2(>2 = 265314, 0*2 = 412563, G 4c2 = 354261 

 <Vi= 5 62I 34, G 2f3 = 516342. G 3c2 = 241635, G 4e3 = 634125 

 Our first standard under 2 (B d is invariable by 



XiX 2 X s , i.e. \\Q>a = (3,j = ^2v?<i = X 3 (3<i > 

 so that O d is four times repeated in (BJ", and has only 15 

 values, as have also those marked out by it. (B 2(? , (5 3(Z , and 

 (3 Irt , having no such symmetry under aa/3/3yy, have 60 

 values ; and all the four standards under 2 have 6 terms. 



ii 2 . The group (356142), (art. 6), has 6=124365 in 

 common with I 8 , which is now divided into products thus : 



I 8 = 123456 x 123456 =HVJ' 2 . 



Xi2i4356 124365 = 9 

 X 2 2i3456 

 XS124356 

 Calling (356142) Gs, we get on it by Xi\ 2 X 3 in H 4 , 

 G u = 6352i4, 6,2 = 365124, 0^=642513, 

 all to be marked out by Gs because they all give ($p: 

 1 1 :; . The group which we take as G2S, 

 G 2 s= 123456 132654 



456231 654321 



23!5 6 4 3 2I 546 



5 6 43 12 546213 



312645 213465 = 9 



645 I2 3 46513 2 



has 213465 in common with Is, which is now written 



I 8 = 123456 x 123456 = H/J 2 " 



X121435 6 213465 = 9 

 X2213456 

 ^124356 

 The preceding H' 4 x J' 2 being altered only in the second 

 factor. By the same X^Xg we get on G 2 S. 



6^ = 532641, G 2£2 = 546i32, 63,3 = 352641, 

 which three are marked out by G 2 §. 



