Right Bol Loop 16.11.4.22 of order 16


0123456789101112131415
1036274591512131011814
2457160310128151491311
3670541213101498151112
4215037612119141581013
5764302115141110131298
6301725411131589141210
7542613014813121110159
8911131215101401263475
9812111014131515436207
1012814911151324051736
1113159141081263507142
1210141581391146170523
1311981512141032715064
1415131011912870342651
1514101213811957624310

Centre:   0   5

Centrum:   0   5   10   11

Nucleus:   0   5

Left Nucleus:   0   5   10   11

Middle Nucleus:   0   5

Right Nucleus:   0   5


Comm(L):   This graph has as its 7 vertices the nontrivial cosets of the centre. Edges represent non-commuting cosets.


1 Element of order 1:   0

11 Elements of order 2:   1   3   4   5   7   8   10   11   12   13   15

4 Elements of order 4:   2   6   9   14

Commutator Subloop:   0   5

Associator Subloop:   0   5

2 Conjugacy Classes of size 1:

7 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:   64 (128, 512)


/ revised October, 2001