Right Bol Loop 16.9.2.12 of order 16


0123456789101112131415
1109011141315122348657
2110910131412151436875
3011109121513144125786
4910110151214133217568
5141512131011907863412
6131215141110098752143
7151413129010115684321
8121314150911106571234
9214365870111013121514
1034128765110914151213
1143217856109015141312
1256871243131415091011
1378654312121514901110
1487563421151213101109
1565782134141312111090

Centre:   0   10

Centrum:   0   10

Nucleus:   0   10

Left Nucleus:   0   10

Middle Nucleus:   0   10

Right Nucleus:   0   10


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:   2   4   9   10   11   12   13   14   15

6 Elements of order 4:   1   3   5   6   7   8

Commutator Subloop:   0   10

Associator Subloop:   0   10

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

Automorphic Inverse Property:   FAILS.   (1-1)(3-1) neq (1*3)-1

Al Property:   FAILS. The left inner mapping L1,1 = (2,4)(5,8)(6,7)(9,11)(12,14)(13,15) is not an automorphism.   L1,1(2*5) neq L1,1(2)*L1,1(5)

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