Right Bol Loop 16.11.2.108 of order 16


0123456789101112131415
1032765498121310111514
2301547610121591481113
3210674511139158141012
4756023113118149151210
5647201315141312111098
6574310214151110131289
7465132012101481591311
8910121315141106437215
9811131214151015342706
1011814151312923016574
1110915141213832650147
1213148911101574105623
1312159810111447561032
1415121011981360724351
1514131110891251273460

Centre:   0   5

Centrum:   0   5

Nucleus:   0   5

Left Nucleus:   0   5

Middle Nucleus:   0   5

Right Nucleus:   0   5


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:   1   2   3   4   5   6   7   8   10   13   15

4 Elements of order 4:   9   11   12   14

Commutator Subloop:   0   5

Associator Subloop:   0   5

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 = (2,4)(3,7)(8,15)(9,14)(10,13)(11,12) is not an automorphism.   L1,8(2*8) neq L1,8(2)*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