Right Bol Loop 16.7.2.58 of order 16


0123456789101112131415
1036725491513121110814
2341670510131581491211
3274501612109148151113
4765032115141110131298
5610347213111491581012
6507214311128159141310
7452163014812131011159
8911131512101407265314
9813101411121510532647
1012814119151323401756
1113159101481265047132
1210981315141136174025
1311141512891052710463
1415121191013874356201
1514101281311941623570

Centre:   0   4

Centrum:   0   4

Nucleus:   0   4

Left Nucleus:   0   4

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. Here we print (in reverse video) the complementary graph, in which edges represent commuting cosets.


1 Element of order 1:   0

7 Elements of order 2:   1   4   7   8   9   14   15

8 Elements of order 4:   2   3   5   6   10   11   12   13

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:   128 (128, 1024)


/ revised October, 2001