Right Bol Loop 16.11.2.133 of order 16


0123456789101112131415
1035247698151314121110
2401673511131481510912
3517062413111291081514
4260715314121110915813
5376104212141315891011
6742530110158141311129
7654321015109121114138
8101214131191501625437
9151411121381010734256
1081312111415967043521
1113151098141223407165
1214891015131154370612
1311108159121432516704
1412915810111345261073
1591113141210876152340

Centre:   0   7

Centrum:   0   7

Nucleus:   0   7

Left Nucleus:   0   7

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

11 Elements of order 2:   1   2   5   6   7   8   9   10   11   12   15

4 Elements of order 4:   3   4   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:   128 (128, 1024)


/ revised October, 2001