Right Bol Loop 16.7.8.0 of order 16


0123456789101112131415
1038109527154131411126
2341061011131251589714
3210135121411146971580
4106503215981141312117
5611231310014112815794
6501210414121337981511
7811415014131019635212
8713119141210401552631
9151214811131047362510
1045918361570121114132
1113156142795312010148
1214871315932611100415
1311915127856214140103
1412721161583513411009
1591407411121108253613

Centre:   0   4   12   13

Centrum:   0   2   4   6   8   9   12   13

Nucleus:   0   4   12   13

Left Nucleus:   0   2   4   6   8   9   12   13

Middle Nucleus:   0   4   12   13

Right Nucleus:   0   4   12   13

1 Element of order 1:   0

7 Elements of order 2:   1   4   10   11   12   13   14

8 Elements of order 4:   2   3   5   6   7   8   9   15

Commutator Subloop:   0   12

Associator Subloop:   0   12

4 Conjugacy Classes of size 1:

6 Conjugacy Classes of size 2:

Automorphic Inverse Property:   FAILS.   (1-1)(3-1) neq (1*3)-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