Right Bol Loop 16.7.4.22 of order 16


0123456789101112131415
1032674598121310111514
2457160310128141591113
3675041213111598141210
4210537612109151481311
5764302114151110131289
6301725411131489151012
7546213015141312111098
8911131214101501624357
9812101115131410342675
1012815911141324507163
1113149151081263051724
1210158141391142715036
1311914812151036170542
1415101213811957263401
1514131110912875436210

Centre:   0   5

Centrum:   0   5   12   13

Nucleus:   0   5

Left Nucleus:   0   5   12   13

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

7 Elements of order 2:   1   5   7   8   9   14   15

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

Commutator Subloop:   0   5

Associator Subloop:   0   5

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

Automorphic Inverse Property:   HOLDS

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