Right Bol Loop 16.11.4.28 of order 16


0123456789101112131415
1230574691181015121314
2301765411109814151213
3012647510811913141512
4576013212131514891110
5764120315121413911108
6457302113141215108911
7645231014151312111089
8911101215131403124675
9111081514121310235467
1089111312141532016754
1110891413151221307546
1215141389101145670123
1312151410811964753012
1413121511109876542301
1514131291181057461230

Centre:   0   2

Centrum:   0   1   2   3

Nucleus:   0   2

Left Nucleus:   0   1   2   3

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

11 Elements of order 2:   2   4   7   8   9   10   11   12   13   14   15

4 Elements of order 4:   1   3   5   6

Commutator Subloop:   0   2

Associator Subloop:   0   2

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

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

Al Property:   FAILS. The left inner mapping L1,8 = (8,11)(9,10) 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:   64 (1024, 2048)


/ revised October, 2001