Right Bol Loop 16.11.4.2 of order 16


0123456789101112131415
1031581042131159146127
2451296011473813101511
3610054114121521381179
4215031011986715141312
5106430213151211497118
6309122510111341571814
7891411131201215465310
8714101151195413231260
9111362127830141515104
1054815136714012112913
1198137141542112010356
1214726913154511100813
1315121114795106832041
1412157131183610951402
1513111108141203764925

Centre:   0   5   11   14

Centrum:   0   5   11   14

Nucleus:   0   5   11   14

Left Nucleus:   0   3   4   5   7   11   13   14

Middle Nucleus:   0   5   11   14

Right Nucleus:   0   5   11   14

1 Element of order 1:   0

11 Elements of order 2:   1   3   4   5   7   9   10   11   12   13   14

4 Elements of order 4:   2   6   8   15

Commutator Subloop:   0   5   11   14

Associator Subloop:   0   14

4 Conjugacy Classes of size 1:

3 Conjugacy Classes of size 4:

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, 256)


/ revised October, 2001