Right Bol Loop 27.14.3.1 of order 27


01234567891011121314151617181920212223242526
12046123119108161714151375192018222321252624
20163174161089751513141112201819232122262425
35781991510012182025262414132122231141261716
41211920101381201918262425151422232116617357
57314101518132624259822232120191204121117166
61716101881492012019242526131523212273541211
73520131891923212215142018102425261211416617
81420012622331612212417472225115618915101319
91518122402147172225561123261612319101381420
10131920251226115232612316212471742081491518
11412181419102021222313150129825262417166735
12114158131914242526109232122182020161716573
13191025262224217470231156121316128142015189
14208262423250561112116123222471791518131910
15189242521261123162227174023611510131914208
16617191520818222321141312010926242557311412
17166139142015252624810212223191801235712114
18915212212324115625231612260174713191020814
19101322232212516123260471724156111420818915
20814232102226717424161152521231615189191013
21222311164712181920176891053131415252624201
22232116761117192018539108124141513262425012
23212271131652018191241089176151314242526120
24252612171154151314616201819371089201222321
25262417516126131415371819204118910012232122
26242551271731415134111920186169108120212223

Centre:   0   21   25

Centrum:   0   21   25

Nucleus:   0   21   25

Left Nucleus:   0   1   2   21   22   23   24   25   26

Middle Nucleus:   0   21   25

Right Nucleus:   0   21   25

1 Element of order 1:   0

14 Elements of order 3:   1   2   3   8   11   13   17   18   21   22   23   24   25   26

12 Elements of order 9:   4   5   6   7   9   10   12   14   15   16   19   20

Commutator Subloop:   0   21   25

Associator Subloop:   0   21   25

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