Right Bol Loop 16.3.4.4 of order 16


0123456789101112131415
1032547615121110914138
2310679121311541015814
3201761291410451181513
4576815131412123011109
5467158141390321101112
6745131410103158212911
7654141301112815391210
8151314129101105674231
9121011103258141315674
1011129231586141013457
1110912328157130114546
1291110012341513148765
1314158101154279126103
1413815111045361297012
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

3 Elements of order 2:   1   8   15

12 Elements of order 4:   2   3   4   5   6   7   9   10   11   12   13   14

Commutator Subloop:   0   1   8   15

Associator Subloop:   0   1   8   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