Right Bol Loop 16.7.2.40 of order 16


0123456789101112131415
1230574698111013121514
2301765411109815141312
3012647510118914151213
4675031212131415891011
5467102314151213101189
6754320113121514981110
7546213015141312111098
8101191514131223107654
9810111315121432015476
1011981412151310236745
1198101213141501324567
1214151311109875642130
1312141591181057463021
1415131210811964751203
1513121489101146570312

Centre:   0   2

Centrum:   0   2

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   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 = (8,11)(9,10) 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