Right Bol Loop 16.1.2.15 of order 16


0123456789101112131415
1032547698111013121514
2310674510118914151312
3201765411109815141213
4567103212131415891011
5476012313121514981110
6754321015141312111089
7645230114151213101198
8910111312151410325476
9811101213141501234567
1011981415121332106754
1110891514131223017645
1213151489111054671023
1312141598101145760132
1415121311108967543210
1514131210119876452301

Centre:   0   1

Centrum:   0   1

Nucleus:   0   1

Left Nucleus:   0   1

Middle Nucleus:   0   1

Right Nucleus:   0   1


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

1 Element of order 2:   1

14 Elements of order 4:   2   3   4   5   6   7   8   9   10   11   12   13   14   15

Commutator Subloop:   0   1

Associator Subloop:   0   1

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

Automorphic Inverse Property:   FAILS.   (2-1)(5-1) neq (2*5)-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