Functions formed an Groups. 49 



has the subgroup J marked in it in common with 



1,6=123456 x 123456 =J B - H 6 



2 3 I 5 6 40i i23564\x 



31264563 123645X2 



13254663 123465X3 



32146564 123654X4 



21365465 123546X5 

 On 



G d = 456312 by Xr "Xs in H 6 



we get the 5 equivalents marked out by G d , which are 

 564231, 645123, 465321, 654213, 546132, or G e r--G e6 . 

 This G rf , being identical with its five derivatives, XxG^, &c, 



under 2, has two terms and 10 values, as have the five 



G e i . . . G e5 . 



The cyclical G D = (234561) has, in common with I 36 ' 



9 = 321654. The index group is 



I 36 = 123456 + X9132564 x 123456 = H 18 -J 2 , 

 Xi23i456 X 10 32i564 321654 = 6 

 X0312456 X U 2 13564 

 X.,132456 X ia i 23645 

 X 4 32i456 X13231645 

 X 5 2 13456 X14312645 

 X 6 i 23564 X 15 i23645 

 X 7 23i564 X 16 32i645 

 X 8 3i2564 Xi 7 2i3645 

 where H 18 =. 1 + X 2 + X 2 4- • ' + X n . 



We obtain on 234561 by H ls the 17 equivalents G Ei " " . 

 Gei7 marked out by G D , which are below headed by G D . 

 2 = aaaftj3(3. 



All these, like -the standard (5 D , have under S 6 terms 

 and 60 values. 

 E 



