Right Bol Loop 16.9.2.285 of order 16


0123456789101112131415
1129141315101102348765
2151213100111491435678
3141109131215104126587
4131491210150113217856
5901114121310158762341
6101312151109147853214
7111015014912136584123
8015101191413125671432
9284617350111015141312
1034857126110914151213
1146513287109013121514
1285672341151413011109
1373286514141512110910
1467124853131215109011
1551738462121314910110

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:   3   6   9   10   11   12   13   14   15

6 Elements of order 4:   1   2   4   5   7   8

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 = (2,5)(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:   128 (1024, 2048)


/ revised October, 2001