Right Bol Loop 28.9.3.0 of order 28

Centre:   0

Centrum:   0   16   26

Nucleus:   0

Left Nucleus:   0   11   16   26

Middle Nucleus:   0   6   10   14   18   22   25

Right Nucleus:   0   6   10   14   18   22   25

1 Element of order 1:   0

9 Elements of order 2:   1   7   11   15   16   19   23   26   27

6 Elements of order 7:   6   10   14   18   22   25

12 Elements of order 14:   2   3   4   5   8   9   12   13   17   20   21   24

Commutator Subloop:   0   6   10   14   18   22   25

Associator Subloop:   0   6   10   14   18   22   25

1 Conjugacy Class of size 1:

•   0

3 Conjugacy Classes of size 2:

•   6   25
•   10   22
•   14   18

3 Conjugacy Classes of size 7:

•   1   7   11   15   19   23   27
•   2   4   8   12   16   20   24
•   3   5   9   13   17   21   26

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

A_l Property:   FAILS. The left inner mapping L_1,1 = (2,16,4,20,8,24,12)(3,13,26,9,21,5,17) is not an automorphism.   L_1,1(2*1) neq L_1,1(2)*L_1,1(1)

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

Right (Left, Full) Mult Group Orders:   56 (9604, 19208)

/ revised November, 2001