Right Bol Loop 16.9.2.298 of order 16


0123456789101112131415
1091110131415122345876
2901011121514131438567
3101190141312154217685
4111009151213143126758
5121314159101108761243
6151413121109107584321
7141512131090116853412
8131215140111095672134
9214387650111013121514
1034126587119014151312
1143217856100915141213
1258671432131415091110
1385762341121514901011
1476854123151312101109
1567583214141213111090

Centre:   0   9

Centrum:   0   9

Nucleus:   0   9

Left Nucleus:   0   9

Middle Nucleus:   0   9

Right Nucleus:   0   9


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:   1   2   6   7   9   12   13   14   15

6 Elements of order 4:   3   4   5   8   10   11

Commutator Subloop:   0   9

Associator Subloop:   0   9

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 = (3,4)(5,8)(6,7)(10,11)(12,13)(14,15) is not an automorphism.   L1,1(3*5) neq L1,1(3)*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