91 
123 564 789 
123 564 897 
123 564 978 
123 456 879 
123 456 987 
123 456 798 
Let this woven group of the order 6 3 be J A ; then 
*Li + Qi J 4 +Q 2 3a is a grouped woven group of 648th order. 
(99) Theorem M. 
Let N— Aft-}- B5-pCc-}- . . -f- J) ; 
A~B B“C C“D 
Let Mjt be the number of groups equivalent to a group G , 
(including G n in this number) formed with R elements, of S B 
substitutions, and such that G.i shall not be equivalent to Gk 
even though A = B. 
Let F r be the entire number of groups, of substitutions, 
that can be formed (containing unity) with r elements. 
We can construct with N elements, upon the given partition 
of N, and with given groups G,i Gjj * * Gj, 
ttN • F„ r„ F e • • F, • • (M// 
7ra ' trb • 7rc " irj • (ttA)" (B) 6 (ttC) 0 * * (ttJ y 
woven grouped groups each of 
(s A )\s JS )Xs c y---(s J yi a i b i c ---i J 
substitutions. 
For example, on the partition, 
10 = 3 • 2 + 2 - 2 = Aa + B5, 
where we have 
we can form 
M, = 1 = M a = F„ 
5T 10 
2 • 2 • 6 2 • 2 * : 
6300 
woven grouped groups, each 
3 2 • 2 2 • 2 • 2 = 144 substitutions, (S 4 = 3), 
or of 
G 2 ■ 2- ■ 2 • 2 = 576 substitutions, (S^ = 6). 
