Right Bol Loop 16.7.2.333 of order 16


0123456789101112131415
1032547698111015141312
2406173510128139111514
3517062411159148101213
4260715312101381415119
5371604215111491312108
6745230113141215108911
7654321014131512119810
8910111215131471534602
9811101512141360425713
1012813914111554761320
1115914813101245670231
1210138149151132107546
1314121510118917352064
1413151211109806243175
1511149138121023016457

Centre:   0   7

Centrum:   0   7

Nucleus:   0   2   5   7

Left Nucleus:   0   1   2   3   4   5   6   7

Middle Nucleus:   0   2   5   7

Right Nucleus:   0   2   5   7


Comm(L):   This graph has as its 7 vertices the nontrivial cosets of the centre. Edges represent non-commuting cosets. Here we print (in reverse video) the complementary graph, in which edges represent 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:   32 (64, 256)


/ revised October, 2001