249 
begun above with one other only system of seven cyclical 
triads, exhausting the duads in seven. Hence r—2, and 
there are thirty equivalent groups of 7’6-4. And as 
we see by the corollary to my theorem A (art. 9, “ Theory of 
Groups,” &c.), that the group has no derived derangement, 
i. e., it is maximum. 
Take next the 55 triads : — * 
124 30 
125 00 
157 38 
2 3 5 47 
267 15 
274 & , 
340 29 
39% 
46(% 
5 70 2o 
60% 
109 3o 
1 7fl 6 o 
160 28 
20a,, 
2 495a 
2 80 35 
378 26 
457 G9 
480 C a 
59 0 48 
68% 
1 3a, 5 
128 7a 
140 57 
29 0 67 
20849 
346 58 
350 1G 
458j 2 
469 10 
59% 
780 19 
189 56 
156 4o 
136 79 
236„ 0 
27a 39 
3 ao 78 
3 /9 50 
45« 30 
568 70 
679^ 
78% 
1«4 89 
1 3 8 4 o 
179 24 
239 1S 
25a G8 
347,„ 
358 98 
489 37 
569 23 
670^ 
89« o2 
which exhaust the duads of eleven elements 12 oa three 
times, and which, disregarding the subindices, fulfil the con- 
dition, that if abc, aid, ale, be three triads, cde is a fourth. 
These 55 triads are formed by a simple cyclical kind of pro- 
cess from the triad 128. The subindex under 124 shows 
that 361, 362 and 364 are triads of the system. 
Each of the 55 triads determines a sextuplet. We form 
on (347 flI ), on (68a 13 ), on (190 3<J ), on (325, 7 ), on (a52 6S ), on (125 90 ), 
13% 
13(3(25 
1 3% 
1 3 ( 3(25 
1 3(Z 2 o 
1 3« 2 5 
670,4 
679^ 
469 10 
24780 
568 70 
290 67 
14% 
13 8 10 
30% 
569 23 
249 5 „ 
4,5 8 12 
2 3 5 47 
25% 
125 90 
347,„ 
68% 
100 3 a 
1 ! 
136 79 
39% 
2 8 0 3 j 
507 2 „ 
267 15 
489 37 ; 
408 g - ; 
780 19 ; 
45 / 69 ; 
26849 '■> 
590,8 ; 
hich are 
all the sextuplets 
containing 
13%. 
The first, 
third, and fifth of (347)„, are the three containing a \ ; the 
second, fourth, and sixth are the three whose subindices are 
the circle 34, 47,73; and so on of the rest. The remaining 
