Right Bol Loop 16.5.2.10 of order 16


0123456789101112131415
1101190151413122348765
2111009141512131437856
3901110131214154216578
4091011121315143125687
5151413129011106784312
6141512130910115873421
7131214151110098652143
8121315141011907561234
9214365870111013121514
1034217865119014151312
1143128756100915141213
1256783421131514091011
1365874312121415901110
1487561234151213101190
1578652143141312111009

Centre:   0   9

Centrum:   0   9

Nucleus:   0   9

Left Nucleus:   0   9

Middle Nucleus:   0   9

Right Nucleus:   0   9


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

5 Elements of order 2:   7   8   9   12   13

6 Elements of order 4:   5   6   10   11   14   15

4 Elements of order 8:   1   2   3   4

Commutator Subloop:   0   9   10   11

Associator Subloop:   0   9   10   11

2 Conjugacy Classes of size 1:

1 Conjugacy Class of size 2:

3 Conjugacy Classes of size 4:

Automorphic Inverse Property:   FAILS.   (1-1)(6-1) neq (1*6)-1

Al Property:   FAILS. The left inner mapping L1,1 = (5,8,6,7)(12,15,13,14) is not an automorphism.   L1,1(1*5) neq L1,1(1)*L1,1(5)

Ar Property:   FAILS. The right inner mapping R1,5 = (1,4)(2,3)(7,8)(10,11)(12,15)(13,14) is not an automorphism.   R1,5(5*12) neq R1,5(5)*R1,5(12)

Right (Left, Full) Mult Group Orders:   64 (4096, 16384)


/ revised October, 2001