Right Bol Loop 24.11.6.0 of order 24

Centre:   0   22

Centrum:   0   5   6   15   19   22

Nucleus:   0   22

Left Nucleus:   0   5   6   10   13   15   19   22

Middle Nucleus:   0   2   4   18   20   22

Right Nucleus:   0   2   4   18   20   22

1 Element of order 1:   0

11 Elements of order 2:   5   6   7   8   10   13   14   15   16   19   22

2 Elements of order 3:   2   4

10 Elements of order 6:   1   3   9   11   12   17   18   20   21   23

Commutator Subloop:   0   2   4

Associator Subloop:   0   2   4

2 Conjugacy Classes of size 1:

•   0
•   22

2 Conjugacy Classes of size 2:

•   2   4
•   18   20

6 Conjugacy Classes of size 3:

•   1   3   5
•   6   9   11
•   7   8   10
•   12   15   17
•   13   14   16
•   19   21   23

Automorphic Inverse Property:   FAILS.   (1^-1)(7^-1) neq (1*7)^-1

A_l Property:   FAILS. The left inner mapping L_1,1 = (6,9,11)(7,10,8)(12,15,17)(13,16,14) is not an automorphism.   L_1,1(1*6) neq L_1,1(1)*L_1,1(6)

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

Right (Left, Full) Mult Group Orders:   48 (648, 1296)

/ revised November, 2001