Right Bol Loop 16.9.2.227 of order 16


0123456789101112131415
1151413111090126384527
2140111312159107435816
3131109151210148162745
4121314159101105217638
5101215140111394726183
6915121011014131853472
7091012131415112548361
8111090141312153671254
9278541630111310121514
1038721456110914151213
1143276581109150141312
1285612347131401591011
1354167832121514901110
1461438725151210131109
1576583214141312111090

Centre:   0   15

Centrum:   0   15

Nucleus:   0   15

Left Nucleus:   0   15

Middle Nucleus:   0   15

Right Nucleus:   0   15


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

9 Elements of order 2:   2   3   5   6   9   10   13   14   15

6 Elements of order 4:   1   4   7   8   11   12

Commutator Subloop:   0   15

Associator Subloop:   0   15

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:   FAILS. The left inner mapping L1,1 = (2,6)(9,14) is not an automorphism.   L1,1(2*3) neq L1,1(2)*L1,1(3)

Ar Property:   HOLDS (i.e. every right inner mapping Ra,b is an automorphism)

Right (Left, Full) Mult Group Orders:   128 (1024, 2048)


/ revised October, 2001