Right Bol Loop 24.9.7.0 of order 24

Centre:   0

Centrum:   0   5   6   14   17   20   23

Nucleus:   0

Left Nucleus:   0   5   6   10   14   17   20   23

Middle Nucleus:   0   2   4

Right Nucleus:   0   2   4

1 Element of order 1:   0

9 Elements of order 2:   5   6   7   8   10   14   17   20   23

2 Elements of order 3:   2   4

12 Elements of order 6:   1   3   9   11   12   13   15   16   18   19   21   22

Commutator Subloop:   0   2   4

Associator Subloop:   0   2   4

1 Conjugacy Class of size 1:

•   0

1 Conjugacy Class of size 2:

•   2   4

7 Conjugacy Classes of size 3:

•   1   3   5
•   6   9   11
•   7   8   10
•   12   15   17
•   13   14   16
•   18   20   22
•   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) 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 (17496, 104976)

/ revised November, 2001