Right Bol Loop 16.3.2.32 of order 16


0123456789101112131415
1230574698111014151213
2301765411109815141312
3012647510118913121514
4675213012131415111098
5467320113121514981110
6754102314151213101189
7546031215141312891011
8101191213141523107654
9810111315121432015476
1011981412151310236745
1198101514131201324567
1213151411910876540132
1315141210118967453201
1412131598111054761023
1514121381091145672310

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   12   15

12 Elements of order 4:   1   3   4   5   6   7   8   9   10   11   13   14

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)(5-1) neq (1*5)-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