Right Bol Loop 16.9.2.441 of order 16


0123456789101112131415
1032547691513121011814
2406173510128159141311
3517062412111498151013
4260715313109141581112
5371604211131581491210
6745230114812131110159
7654321015141110131298
8911121310141576523410
9813101112151460342571
1013151498121154701632
1112891415131023076145
1211141589101342160753
1310981514111235617024
1415121110138917435206
1514101312119801254367

Centre:   0   7

Centrum:   0   7

Nucleus:   0   7

Left Nucleus:   0   7

Middle Nucleus:   0   7

Right Nucleus:   0   7


Comm(L):   This graph has as its 7 vertices the nontrivial cosets of the centre. Edges represent non-commuting cosets. Here we print (in reverse video) the complementary graph, in which edges represent commuting cosets.


1 Element of order 1:   0

9 Elements of order 2:   1   2   5   6   7   9   12   13   14

6 Elements of order 4:   3   4   8   10   11   15

Commutator Subloop:   0   7

Associator Subloop:   0   7

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:   HOLDS (i.e. every left inner mapping La,b is an automorphism)

Ar Property:   HOLDS (i.e. every right inner mapping Ra,b is an automorphism)

Right (Left, Full) Mult Group Orders:   128 (128, 1024)


/ revised October, 2001