Right Bol Loop 16.7.4.1 of order 16


0123456789101112131415
1032547615121110914138
2310674513111291015814
3201765414109121181513
4567815231211314010119
5476158329014131111012
6754131401103815291211
7645141310112158312910
8151314129101105674231
9121110101413583215764
1011912238156140113547
1110129321587131014456
1291011011314415238675
1314158101112927456103
1413815111091236547012
1581413912111014765320

Centre:   0   1   8   15

Centrum:   0   1   8   15

Nucleus:   0   1   8   15

Left Nucleus:   0   1   8   15

Middle Nucleus:   0   1   8   15

Right Nucleus:   0   1   8   15

1 Element of order 1:   0

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

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

Commutator Subloop:   0   1   8   15

Associator Subloop:   0   1   8   15

4 Conjugacy Classes of size 1:

2 Conjugacy Classes of size 2:

2 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