Right Bol Loop 8.1.4.0 of order 8


01234567
17506243
26750314
30675421
45067132
52341706
64123075
73412650

Centre:   0   7

Centrum:   0   5   6   7

Nucleus:   0   7

Left Nucleus:   0   5   6   7

Middle Nucleus:   0   7

Right Nucleus:   0   7

1 Element of order 1:   0

1 Element of order 2:   7

6 Elements of order 4:   1   2   3   4   5   6

Commutator Subloop:   0   7

Associator Subloop:   0   7

2 Conjugacy Classes of size 1:

3 Conjugacy Classes of size 2:

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

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:   16 (32, 64)


/ revised November, 2001