Right Bol Loop 16.7.4.42 of order 16


0123456789101112131415
1036725491581314111210
2341670511121315910814
3274501612141191581013
4765032115109141312118
5610347213111410815912
6507214314131281091511
7452163010815121114139
8101112151314941765320
9151214101113874032651
1081311914121510456237
1113159141081263507142
1214101513891156270413
1311981215101432614075
1412810119151325341706
1591413812111007123564

Centre:   0   4

Centrum:   0   4   11   14

Nucleus:   0   4

Left Nucleus:   0   4   11   14

Middle Nucleus:   0   4

Right Nucleus:   0   4


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   4   7   11   12   13   14

8 Elements of order 4:   2   3   5   6   8   9   10   15

Commutator Subloop:   0   4

Associator Subloop:   0   4

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

Automorphic Inverse Property:   HOLDS

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