Right Bol Loop 24.5.12.0 of order 24


01234567891011121314151617181920212223
11618201419013151723222126345987101211
21522211723131401620191865134121110987
31721231322150161419182012456101211798
41420190181615171322212331562798111012
51323221521171614018201943621111012879
60191816201417131521232254213879121110
71914018162021232215171310911812641253
81801620141923222117131511712910164325
92016141901822212313151712810711416532
10231713221521182019016149127118532641
11221315211723201918161407108129253164
12211517231322191820140168119107325416
13261345101112978141701516222321181920
14652134978121011171613015192018222321
15314562111210789013161714212223201819
16435621897111210150171413201819232122
17546213121011897161514130232122192018
18912107118614523221921202316014171513
19811129107461352232022182101416151317
20710118129146235211823192214160131715
21109711812235614182220231917151314160
22128910711523461192318212015131716014
23117812910352146202119221813171501416

Centre:   0   14   16   21   22   23

Centrum:   0   13   14   15   16   17   18   19   20   21   22   23

Nucleus:   0   14   16   21   22   23

Left Nucleus:   0   13   14   15   16   17   18   19   20   21   22   23

Middle Nucleus:   0   14   16   21   22   23

Right Nucleus:   0   14   16   21   22   23

1 Element of order 1:   0

5 Elements of order 2:   4   10   17   20   22

2 Elements of order 3:   14   16

2 Elements of order 4:   2   8

10 Elements of order 6:   1   6   11   12   13   15   18   19   21   23

4 Elements of order 12:   3   5   7   9

Commutator Subloop:   0   22

Associator Subloop:   0   22

6 Conjugacy Classes of size 1:

9 Conjugacy Classes of size 2:

Automorphic Inverse Property:   FAILS.   (1-1)(3-1) neq (1*3)-1

Al Property:   HOLDS (i.e. every left inner mapping La,b is an automorphism)

Ar Property:   HOLDS (i.e. every right inner mapping Ra,b is an automorphism)

Right (Left, Full) Mult Group Orders:   48 (96, 192)


/ revised November, 2001