Right Bol Loop 16.7.2.248 of order 16


0123456789101112131415
1230574691181015121314
2301765411109814151213
3012647510811913141512
4675231012131514810119
5467302113141215101198
6754120315121413981011
7546013214151312119810
8911101215131401324576
9111081312141512036457
1089111514121330215764
1110891413151223107645
1215141311910845670321
1312151410118957463210
1413121581091176542103
1514131298111064751032

Centre:   0   2

Centrum:   0   2

Nucleus:   0   2

Left Nucleus:   0   2

Middle Nucleus:   0   2

Right Nucleus:   0   2


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

7 Elements of order 2:   2   5   6   8   11   12   14

8 Elements of order 4:   1   3   4   7   9   10   13   15

Commutator Subloop:   0   2

Associator Subloop:   0   2

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

Automorphic Inverse Property:   FAILS.   (4-1)(9-1) neq (4*9)-1

Al Property:   FAILS. The left inner mapping L1,8 = (4,7)(5,6) is not an automorphism.   L1,8(4*8) neq L1,8(4)*L1,8(8)

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