Right Bol Loop 27.8.3.1 of order 27


01234567891011121314151617181920212223242526
12041119151214168317610131879205222321262425
20151913414161292010318111787615232122252624
34671814172421220911221023252616813515191120
46312177162625011022142482123218951513201911
51513141612182502628247219221231710192011643
63417101882224212512231611422609715135112019
78142421222194113252026501561323118910161712
81471220244111913235251521203626291018121617
91018202115152011263231322641925241612171487
10189026252231361524111231952024211217167148
11192097812223122180102617252124141634651315
12171626224232051540622311319112125147818109
13515814107122321162590182624221217111920436
14782524126631352119042112015222310189171216
15135101291402625231721822162421718201119364
16121723122515205192213216243114026814710918
17161222232621111946115242025513320781491810
18910212523013632024112192641551221716128714
19201116817923122414261825702221101246315513
20111918916102122242672172312102581463413155
21222313631989718151451620121017411252426102
22232111320139781741615126141810519242625210
23212215131151018171668209197141234262524021
24262519206111612147518417310981513120232221
25242661542017101814137198591216113012222123
26252420515318171012199117481614136201212322

Centre:   0   23   24

Centrum:   0   23   24

Nucleus:   0   23   24

Left Nucleus:   0   4   9   13   14   17   20   23   24

Middle Nucleus:   0   23   24

Right Nucleus:   0   23   24

1 Element of order 1:   0

8 Elements of order 3:   1   2   21   22   23   24   25   26

18 Elements of order 9:   3   4   5   6   7   8   9   10   11   12   13   14   15   16   17   18   19   20

Commutator Subloop:   0   23   24

Associator Subloop:   0   23   24

3 Conjugacy Classes of size 1:

8 Conjugacy Classes of size 3:

Automorphic Inverse Property:   HOLDS

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:   81 (243, 2187)


/ revised October, 2001