Right Bol Loop 16.9.4.32 of order 16


0123456789101112131415
1121513149101105348672
2151211100141398435761
3131412151109107126854
4141390101512116217583
5901413121110151762438
6101109141215134853127
7111015121390143584216
8091011151314122671345
9217684350111015141312
1034127856110913121514
1143586217109014151213
1285672341151314010119
1367854123141215100911
1476213584131512119010
1558431762121413911100

Centre:   0   12

Centrum:   0   10   12   13

Nucleus:   0   12

Left Nucleus:   0   10   12   13

Middle Nucleus:   0   12

Right Nucleus:   0   12


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

9 Elements of order 2:   4   7   9   10   11   12   13   14   15

6 Elements of order 4:   1   2   3   5   6   8

Commutator Subloop:   0   12

Associator Subloop:   0   12

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 L1,1 = (2,5)(9,15) is not an automorphism.   L1,1(2*3) neq L1,1(2)*L1,1(3)

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