Right Bol Loop 16.7.4.34 of order 16


0123456789101112131415
1035247691581413121110
2401673511141381591012
3517062413111210915814
4260715314121191081513
5376104212131415810911
6742530110815131411129
7654321015109121114138
8101214131191576152340
9151411121381060734521
1081312111415917043256
1113151098141253470162
1214891015131124307615
1311108159121445216703
1412915810111332561074
1591113141210801625437

Centre:   0   7

Centrum:   0   7   9   10

Nucleus:   0   7

Left Nucleus:   0   7   9   10

Middle Nucleus:   0   7

Right Nucleus:   0   7


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   2   5   6   7   9   10

8 Elements of order 4:   3   4   8   11   12   13   14   15

Commutator Subloop:   0   7

Associator Subloop:   0   7

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