Right Bol Loop 16.7.2.261 of order 16


0123456789101112131415
1230574698111013121514
2301765411109815141312
3012647510118914151213
4576231012131415111098
5764302114151213981110
6457120313121514101189
7645013215141312891011
8101191513141221304567
9810111312151430216745
1011981415121312035476
1198101214131503127654
1213151489101176542130
1315141210811954763021
1412131591181067451203
1514121311109845670312

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   5   6   9   10   13   14

8 Elements of order 4:   1   3   4   7   8   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.   (4-1)(9-1) neq (4*9)-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