Right Bol Loop 16.11.2.112 of order 16


0123456789101112131415
1230574698111013121514
2301765411109815141312
3012647510118914151213
4576031212131415810911
5764102313121514911810
6457320114151213108119
7645213015141312119108
8101191514131221304657
9810111412151330215746
1011981315121412036475
1198101213141503127564
1214151311910875640132
1312141510118964751023
1415131298111057463201
1513121481091146572310

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

11 Elements of order 2:   2   4   5   6   7   9   10   12   13   14   15

4 Elements of order 4:   1   3   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) 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