Right Bol Loop 16.9.2.268 of order 16


0123456789101112131415
1151410111290136854327
2140121310159117538416
3131115914121004726158
4121391501011143671285
5111014015131298217634
6915111013014121483572
7091312111415102345861
8101201491113155162743
9275831640111310121514
1035726481120149151113
1143271856139015141012
1258617342101415091311
1384162537111591401210
1461438725151210131109
1576854213141312111090

Centre:   0   15

Centrum:   0   15

Nucleus:   0   15

Left Nucleus:   0   15

Middle Nucleus:   0   15

Right Nucleus:   0   15


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

9 Elements of order 2:   2   6   9   10   11   12   13   14   15

6 Elements of order 4:   1   3   4   5   7   8

Commutator Subloop:   0   15

Associator Subloop:   0   15

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:   FAILS. The left inner mapping L1,1 = (2,6)(9,14) is not an automorphism.   L1,1(2*3) neq L1,1(2)*L1,1(3)

Ar Property:   HOLDS (i.e. every right inner mapping Ra,b is an automorphism)

Right (Left, Full) Mult Group Orders:   128 (1024, 2048)


/ revised October, 2001