Right Bol Loop 16.7.4.36 of order 16


0123456789101112131415
1032547691411151081312
2406173510121491311158
3517062411101314815129
4260715312159814101113
5371604215118139121014
6745230113812101514911
7654321014131512119810
8910111215131401234675
9811101512141317352064
1012813914111524716350
1115914813101232670541
1210138149151145107236
1314121510118960425713
1413151211109876543102
1511149138121053061427

Centre:   0   7

Centrum:   0   7   8   14

Nucleus:   0   7

Left Nucleus:   0   7   8   14

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

7 Elements of order 2:   1   2   5   6   7   8   14

8 Elements of order 4:   3   4   9   10   11   12   13   15

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:   64 (128, 512)


/ revised October, 2001