Right Bol Loop 16.9.2.74 of order 16


0123456789101112131415
1091411131015127358462
2901114101312158467351
3101309151211145826714
4111415120910136715823
5131090121514113284176
6141112159013104173285
7151213101411091532648
8121510131114902641537
9215634870111015141312
1035827146111215149013
1146281735101512130914
1287654321151413011109
1353718264149011121510
1464172853130910151211
1578436512121314910110

Centre:   0   12

Centrum:   0   12

Nucleus:   0   12

Left Nucleus:   0   12

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

9 Elements of order 2:   1   2   3   6   7   8   9   12   15

6 Elements of order 4:   4   5   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)(4-1) neq (1*4)-1

Al Property:   FAILS. The left inner mapping L1,1 = (2,7)(3,6)(4,5)(9,15)(10,14)(11,13) 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