Right Bol Loop 16.7.2.81 of order 16


0123456789101112131415
1230547698111014121513
2301765411109815141312
3012674510118913151214
4576213012131415810911
5764302114151213981110
6457120313121514101189
7645031215141312119108
8101191514131221307564
9810111312151430216745
1011981415121312035476
1198101213141503124657
1213151489101176542130
1315141210118954761023
1412131598111067453201
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 = (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