Right Bol Loop 16.3.8.3 of order 16


0123456789101112131415
1250367491381014121511
2561074313129815141110
3014725610811151391214
4307612511101514981312
5672143012141391115108
6745230114151213101189
7436501215111412810913
8913101112141523701645
9131281014151150412736
1089111513121414630572
1110815149131207543261
1214151391110872056314
1312149815111061325407
1415111213108945167023
1511101412891336274150

Centre:   0   2   4   6

Centrum:   0   1   2   3   4   5   6   7

Nucleus:   0   2   4   6

Left Nucleus:   0   1   2   3   4   5   6   7

Middle Nucleus:   0   2   4   6

Right Nucleus:   0   2   4   6

1 Element of order 1:   0

3 Elements of order 2:   6   9   15

4 Elements of order 4:   2   4   10   12

8 Elements of order 8:   1   3   5   7   8   11   13   14

Commutator Subloop:   0   6

Associator Subloop:   0   6

4 Conjugacy Classes of size 1:

6 Conjugacy Classes of size 2:

Automorphic Inverse Property:   FAILS.   (1-1)(9-1) neq (1*9)-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 (64, 128)


/ revised October, 2001