Right Bol Loop 16.7.4.65 of order 16


0123456789101112131415
1230547691181014151213
2301765411109815141312
3012674510811913121514
4576231012141315119108
5764320114151213108119
6457102313121514911810
7645013215131412810911
8101191214131523107564
9810111412151330216475
1011981315121412035746
1198101513141201324657
1213151411109876540312
1315141298111057463021
1412131510118964751203
1514121389101145672130

Centre:   0   2

Centrum:   0   2   4   7

Nucleus:   0   2

Left Nucleus:   0   2   4   7

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   9   10   12   13   14   15

8 Elements of order 4:   1   3   4   5   6   7   8   11

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