Right Bol Loop 16.7.4.29 of order 16


0123456789101112131415
1032547698121510141311
2406173510118913121514
3517062411101314815129
4260715312159814101113
5371604215121413911108
6745230113141110158912
7654321014131512119810
8910111215131471534602
9811101512141360352714
1012813914111553716420
1115914813101242170536
1210138149151135607241
1314121510118917425063
1413151211109806243175
1511149138121024061357

Centre:   0   7

Centrum:   0   7   10   15

Nucleus:   0   7

Left Nucleus:   0   7   10   15

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   9   13

8 Elements of order 4:   3   4   8   10   11   12   14   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