Right Bol Loop 16.7.4.62 of order 16


0123456789101112131415
1035247691581314111210
2401673511141315810912
3517062413111210915814
4260715314121191081513
5376104212131481591011
6742530110815141312119
7654321015109121114138
8101213141191501625347
9151412111381017034256
1081311121415960743521
1113159108141224370615
1214810915131153407162
1311101589121432561704
1412981510111345216073
1591114131210876152430

Centre:   0   7

Centrum:   0   7   13   14

Nucleus:   0   7

Left Nucleus:   0   7   13   14

Middle Nucleus:   0   7

Right Nucleus:   0   7


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

7 Elements of order 2:   1   2   5   6   7   8   15

8 Elements of order 4:   3   4   9   10   11   12   13   14

Commutator Subloop:   0   7

Associator Subloop:   0   7

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:   HOLDS (i.e. every left inner mapping La,b is an automorphism)

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

Right (Left, Full) Mult Group Orders:   64 (128, 512)


/ revised October, 2001