Right Bol Loop 16.3.4.0 of order 16


0123456789101112131415
1032548967151211141310
2310684125111397151014
3201865114121479101513
4579101513214312106811
5497151014313211018612
6811121314100151732549
7954230101156141311128
8612111413151100923457
9745321150108131412116
1015131412117698054231
1112861031421351015974
1211680121331441510795
1314151079124115286103
1413101597115124368012
1510141311129876145320

Centre:   0   1   10   15

Centrum:   0   1   10   15

Nucleus:   0   1   10   15

Left Nucleus:   0   1   10   15

Middle Nucleus:   0   1   10   15

Right Nucleus:   0   1   10   15

1 Element of order 1:   0

3 Elements of order 2:   1   10   15

12 Elements of order 4:   2   3   4   5   6   7   8   9   11   12   13   14

Commutator Subloop:   0   1   10   15

Associator Subloop:   0   1   10   15

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