Right Bol Loop 24.9.1.0 of order 24


01234567891011121314151617181920212223
11615171413018201921222376849325101112
21501617141322212318192011510312164879
31716141301521232220181910212511416798
41417130151620191823212281967532111210
51314015161723222119201812311210641987
60131516171419182022232194718253121011
71822212023190161415131769184101112325
82021231922181614017151317496121011253
91923221821201401613171548671111210532
10211820231922151713160142113125879164
11221918212023131517014165122103798416
12232019221821171315141603105112987641
13261345111012798141701516222321201819
14652134978111210171613015192018232122
15314562101211879013161714212223181920
16435621897121011150171413201819222321
17546213121110987161514130232122192018
18810129117146325221921202316014151317
19711108129614253232022182101416171513
20912117108461532211823192214160131715
21128911710352416182220231917151301416
22107812911235164192318212015131716014
23119710812523641202119221813171514160

Centre:   0

Centrum:   0

Nucleus:   0

Left Nucleus:   0   17   20   22

Middle Nucleus:   0   14   16

Right Nucleus:   0   14   16

1 Element of order 1:   0

9 Elements of order 2:   2   4   7   12   17   20   21   22   23

2 Elements of order 3:   14   16

12 Elements of order 6:   1   3   5   6   8   9   10   11   13   15   18   19

Commutator Subloop:   0   14   16   21   22   23

Associator Subloop:   0   14   16   21   22   23

1 Conjugacy Class of size 1:

1 Conjugacy Class of size 2:

1 Conjugacy Class of size 3:

3 Conjugacy Classes of size 6:

Automorphic Inverse Property:   FAILS.   (1-1)(11-1) neq (1*11)-1

Al Property:   FAILS. The left inner mapping L1,1 = (2,7)(3,8)(5,9)(10,11,12)(13,19)(15,18)(17,20)(21,23,22) is not an automorphism.   L1,1(1*10) neq L1,1(1)*L1,1(10)

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

Right (Left, Full) Mult Group Orders:   96 (69984, 839808)


/ revised November, 2001