Right Bol Loop 16.9.2.75 of order 16


0123456789101112131415
1032547698121510141311
2406173510118913121514
3517062411101314815129
4260715312159814101113
5371604215121413911108
6745230113141110158912
7654321014131512119810
8910121115131476243105
9811151012141367425013
1012891314111554061327
1115981413101245607231
1210131489151132170546
1314121015118910352764
1413151112109801534672
1511141398121023716450

Centre:   0   7

Centrum:   0   7

Nucleus:   0   7

Left Nucleus:   0   7

Middle Nucleus:   0   7

Right Nucleus:   0   7


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

9 Elements of order 2:   1   2   5   6   7   10   11   12   15

6 Elements of order 4:   3   4   8   9   13   14

Commutator Subloop:   0   7

Associator Subloop:   0   7

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

Automorphic Inverse Property:   FAILS.   (1-1)(3-1) neq (1*3)-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