Right Bol Loop 16.3.4.27 of order 16


0123456789101112131415
1036725498111310121514
2341670510118149151213
3274501611109815141312
4765032115141312111098
5610347212131415891011
6507214313121591481110
7452163014151210131189
8910111512131447653210
9811131410121574526301
1011159131481265417032
1110141512891356740123
1213981115141032104765
1312814109151123071456
1415121091311810362547
1514131281110901235674

Centre:   0   4

Centrum:   0   4   8   15

Nucleus:   0   4

Left Nucleus:   0   4   8   15

Middle Nucleus:   0   4

Right Nucleus:   0   4


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

3 Elements of order 2:   1   4   7

12 Elements of order 4:   2   3   5   6   8   9   10   11   12   13   14   15

Commutator Subloop:   0   4

Associator Subloop:   0   4

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

Automorphic Inverse Property:   FAILS.   (2-1)(9-1) neq (2*9)-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:   64 (128, 512)


/ revised October, 2001