Right Bol Loop 16.7.4.11 of order 16


0123456789101112131415
1032548967131211101514
2310681241151597141013
3201861151241479151310
4579101315214312101186
5497131014315211011268
6811121514010113732945
7954231001316141581211
8612111415113010923754
9745321311008151461112
1013151412117698054132
1112861031421551013479
1211680121531441310597
1310141511129876145023
1415101397511412368210
1514131079412511286301

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

7 Elements of order 2:   1   6   7   8   9   10   13

8 Elements of order 4:   2   3   4   5   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