Right Bol Loop 16.7.2.319 of order 16


0123456789101112131415
1032574698111013151214
2301647510118914121513
3210765411109815141312
4657021312131415891011
5746103214151213108119
6475230113121514911810
7564312015141312111098
8910111214131532107654
9811101415121323015746
1011891312151410326475
1110981513141201234567
1213141581091175643120
1312151410118957462301
1415121398111064751032
1514131211910846570213

Centre:   0   3

Centrum:   0   3

Nucleus:   0   3

Left Nucleus:   0   3   4   7

Middle Nucleus:   0   3

Right Nucleus:   0   3


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:   1   2   3   4   5   6   7

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

Commutator Subloop:   0   3

Associator Subloop:   0   3

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

Automorphic Inverse Property:   HOLDS

Al Property:   FAILS. The left inner mapping L1,8 = (12,15)(13,14) 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