Right Bol Loop 16.7.4.45 of order 16


0123456789101112131415
1230574698111013121514
2301765411109815141312
3012647510118914151213
4576013212131415891011
5764120313121514981110
6457302114151213101189
7645231015141312111098
8101191213141521304657
9810111315121430215746
1011981412151312036475
1198101514131203127564
1214151389101175640312
1312141591181064751203
1415131210811957463021
1513121411109846572130

Centre:   0   2

Centrum:   0   2   4   7

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   7   9   10   12   15

8 Elements of order 4:   1   3   5   6   8   11   13   14

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:   64 (1024, 2048)


/ revised October, 2001