Right Bol Loop 16.3.4.1 of order 16


0123456789101112131415
1032548967131211101514
2310681141251479151310
3201861251141597141013
4579101314315212101186
5497131015214311011268
6812111415110013932745
7954321011308141561112
8611121514013110723954
9745231301016151481211
1013141512119876054123
1112681031421551013497
1211860121531441310579
1310151411127698145032
1415131097512411286310
1514101379411512368201

Centre:   0   1   10   13

Centrum:   0   1   10   13

Nucleus:   0   1   10   13

Left Nucleus:   0   1   10   13

Middle Nucleus:   0   1   10   13

Right Nucleus:   0   1   10   13

1 Element of order 1:   0

3 Elements of order 2:   1   10   13

12 Elements of order 4:   2   3   4   5   6   7   8   9   11   12   14   15

Commutator Subloop:   0   1   10   13

Associator Subloop:   0   1   10   13

4 Conjugacy Classes of size 1:

3 Conjugacy Classes of size 4:

Automorphic Inverse Property:   FAILS.   (2-1)(5-1) neq (2*5)-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