Right Bol Loop 16.11.4.3 of order 16


0123456789101112131415
1036725131011891514412
2309181210134714615115
3211012111587141345096
4149121008156253131117
5615110101914741331282
6512815901141314721103
7131015811103526149124
8101314274301211596511
9114761413512015182310
1087135414211501211369
1191443137615112010528
1215651332149811100471
1378011129126354101514
1441119151012536278013
1512521463411109817130

Centre:   0   10   11   12

Centrum:   0   10   11   12

Nucleus:   0   10   11   12

Left Nucleus:   0   10   11   12

Middle Nucleus:   0   10   11   12

Right Nucleus:   0   10   11   12

1 Element of order 1:   0

11 Elements of order 2:   1   2   6   7   8   9   10   11   12   14   15

4 Elements of order 4:   3   4   5   13

Commutator Subloop:   0   10   11   12

Associator Subloop:   0   10   11   12

4 Conjugacy Classes of size 1:

2 Conjugacy Classes of size 2:

2 Conjugacy Classes of size 4:

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:   32 (256, 1024)


/ revised October, 2001