Right Bol Loop 27.20.3.1 of order 27


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Centre:   0   1   2

Centrum:   0   1   2

Nucleus:   0   1   2

Left Nucleus:   0   1   2   3   4   5   6   7   8

Middle Nucleus:   0   1   2

Right Nucleus:   0   1   2

1 Element of order 1:   0

20 Elements of order 3:   1   2   9   10   11   12   13   14   15   16   17   18   19   20   21   22   23   24   25   26

6 Elements of order 9:   3   4   5   6   7   8

Commutator Subloop:   0   1   2

Associator Subloop:   0   1   2

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