Right Bol Loop 16.11.2.103 of order 16


0123456789101112131415
1032574698111014121513
2301647510118913151214
3210765411109815141312
4657021312131415891011
5746103214151213911810
6475230113121514108119
7564312015141312111098
8910111514131231207654
9811101315121420316475
1011891412151313025746
1110981213141502134567
1213141511109876543120
1312151491181054761032
1415121310811967452301
1514131289101145670213

Centre:   0   3

Centrum:   0   3

Nucleus:   0   3

Left Nucleus:   0   3   4   7

Middle Nucleus:   0   3

Right Nucleus:   0   3


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:   1   2   3   4   5   6   7   9   10   13   14

4 Elements of order 4:   8   11   12   15

Commutator Subloop:   0   3

Associator Subloop:   0   3

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:   64 (1024, 2048)


/ revised October, 2001