Right Bol Loop 16.11.4.27 of order 16


0123456789101112131415
1032765491513108141112
2301674510118913121514
3210547611141281015913
4765032113109151481211
5674301215121413911108
6547210312811141510139
7456123014131512119810
8121013111591401736425
9151114101281315320746
1013812914111523514607
1114915813101237102564
1281310149151160475231
1310128151114942657013
1411159121013874063152
1591411138121056241370

Centre:   0   5

Centrum:   0   2   5   7

Nucleus:   0   5

Left Nucleus:   0   2   5   7

Middle Nucleus:   0   5

Right Nucleus:   0   5


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

11 Elements of order 2:   1   2   3   4   5   6   7   8   11   13   15

4 Elements of order 4:   9   10   12   14

Commutator Subloop:   0   5

Associator Subloop:   0   5

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

Automorphic Inverse Property:   FAILS.   (1-1)(9-1) neq (1*9)-1

Al Property:   FAILS. The left inner mapping L1,8 = (8,15)(9,12) is not an automorphism.   L1,8(2*8) neq L1,8(2)*L1,8(8)

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