Right Bol Loop 16.3.2.101 of order 16


0123456789101112131415
1032674598151413121110
2457160311141289151013
3675041214111398101512
4210537612131110159814
5764302115109131411128
6301725413121415108911
7546213010158121114139
8101114121513957164230
9151411131012875046321
1081213119141510532467
1114151091381264351072
1213981514101132615704
1312891011151423407516
1411101581291346270153
1591312148111001723645

Centre:   0   5

Centrum:   0   5

Nucleus:   0   5

Left Nucleus:   0   1   5   7

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