Right Bol Loop 16.3.2.28 of order 16


0123456789101112131415
1230574698111013121514
2301765411109815141312
3012647510118914151213
4576231012131415891011
5764302113121514981110
6457120314151213101189
7645013215141312111098
8101191213141523107654
9810111315121432016745
1011981412151310235476
1198101514131201324567
1214151311109876542310
1312141510811967453201
1415131291181054761023
1513121489101145670132

Centre:   0   2

Centrum:   0   2

Nucleus:   0   2

Left Nucleus:   0   2

Middle Nucleus:   0   2

Right Nucleus:   0   2


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:   2   5   6

12 Elements of order 4:   1   3   4   7   8   9   10   11   12   13   14   15

Commutator Subloop:   0   2

Associator Subloop:   0   2

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

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

Al Property:   FAILS. The left inner mapping L1,8 = (4,7)(5,6)(8,11)(9,10)(12,15)(13,14) is not an automorphism.   L1,8(4*8) neq L1,8(4)*L1,8(8)

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