Right Bol Loop 16.9.4.31 of order 16


0123456789101112131415
1101109141315122348756
2111090151214131436578
3091011121513144125687
4901110131412153217865
5141312150911107863214
6131415121110098752341
7151213149010115684123
8121514131011906571432
9214378560111013121514
1034128765110914151213
1143216587109015141312
1256873421131415091011
1378654312121514901110
1487561243151213101109
1565782134141312111090

Centre:   0   10

Centrum:   0   9   10   11

Nucleus:   0   10

Left Nucleus:   0   9   10   11

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:   5   8   9   10   11   12   13   14   15

6 Elements of order 4:   1   2   3   4   6   7

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)(6-1) neq (1*6)-1

Al Property:   FAILS. The left inner mapping L1,1 = (5,8)(12,14) 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:   64 (1024, 2048)


/ revised October, 2001