Right Bol Loop 16.5.4.15 of order 16


0123456789101112131415
1015141113109122648537
2912111410130151537648
3101312915011144176285
4111491201510133285176
5131015012914116714823
6141101591213105823714
7150131014111298462351
8129101311141507351462
9215634870111015141312
1034127856111215149013
1143781265101512130914
1287654321151413011109
1356218734149011121510
1465872143130910151211
1578436512121314910110

Centre:   0   12

Centrum:   0   11   12   13

Nucleus:   0   12

Left Nucleus:   0   11   12   13

Middle Nucleus:   0   12

Right Nucleus:   0   12


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

5 Elements of order 2:   1   8   9   12   15

10 Elements of order 4:   2   3   4   5   6   7   10   11   13   14

Commutator Subloop:   0   12

Associator Subloop:   0   12

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 = (2,7)(9,15) 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:   64 (1024, 2048)


/ revised October, 2001