Right Bol Loop 16.3.4.32 of order 16


0123456789101112131415
1032674598111013121514
2457160310138914151211
3675041213101514981112
4210537611129815141310
5764302114151213101189
6301725412111415891013
7546213015141312111098
8910131114121557632401
9813101215111475364210
1011141591281364570123
1110981413151232751046
1213891510141123015764
1312151481191046107532
1415121113810901246357
1514111210913810423675

Centre:   0   5

Centrum:   0   5   8   14

Nucleus:   0   5

Left Nucleus:   0   5   8   14

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

3 Elements of order 2:   1   5   7

12 Elements of order 4:   2   3   4   6   8   9   10   11   12   13   14   15

Commutator Subloop:   0   5

Associator Subloop:   0   5

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

Automorphic Inverse Property:   FAILS.   (2-1)(9-1) neq (2*9)-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