Right Bol Loop 16.7.2.254 of order 16


0123456789101112131415
1230574691181014121513
2301765411109815141312
3012647510811913151214
4576031212141315891011
5764102314151213911810
6457320113121514108119
7645213015131412111098
8101191214131523107564
9810111415121330216745
1011981312151412035476
1198101513141201324657
1213151481091176542310
1315141210118957461203
1412131598111064753021
1514121311910845670132

Centre:   0   2

Centrum:   0   2

Nucleus:   0   2

Left Nucleus:   0   1   2   3

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

7 Elements of order 2:   2   4   5   6   7   9   10

8 Elements of order 4:   1   3   8   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)(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:   64 (1024, 2048)


/ revised October, 2001