Right Bol Loop 16.7.2.153 of order 16


0123456789101112131415
1230547698111013151214
2301765411109815141312
3012674510118914121513
4576013212131415111098
5764102314151213911810
6457320113121514108119
7645231015141312891011
8101191513141223104657
9810111315121432016745
1011981412151310235476
1198101214131501327564
1213151411109875642310
1315141298111057463021
1412131510118964751203
1514121389101146570132

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

7 Elements of order 2:   2   4   5   6   7   13   14

8 Elements of order 4:   1   3   8   9   10   11   12   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:   128 (1024, 2048)


/ revised October, 2001