Right Bol Loop 16.7.2.255 of order 16


0123456789101112131415
1036725491512131011814
2341670510111591481213
3274501611139158141012
4765032115141312111098
5610347212101481591311
6507214313128149151110
7452163014811101312159
8910121511131407235614
9811101413121510562347
1011151413981225417036
1110148121591332140765
1213915118141056704123
1312891014151163071452
1415121391011874326501
1514131181210941653270

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