Right Bol Loop 16.15.2.25 of order 16


0123456789101112131415
1035247968151211141310
2306174510118131415129
3210765114101389121514
4567012153129141310118
5471603212151498111013
6742530131141110158912
7654321014131215109811
8910111512131401235674
9811121015141130453762
1011813914151223067451
1110981413123152601547
1215149138111054710326
1314151012118697324015
1413121511109876542103
1512131489104115176230

Centre:   0

Centrum:   0   14

Nucleus:   0

Left Nucleus:   0   7   8   14

Middle Nucleus:   0

Right Nucleus:   0

1 Element of order 1:   0

15 Elements of order 2:   1   2   3   4   5   6   7   8   9   10   11   12   13   14   15

Commutator Subloop:   0   7   8   14

Associator Subloop:   0   7   8   14

1 Conjugacy Class of size 1:

1 Conjugacy Class of size 3:

3 Conjugacy Classes of size 4:

Automorphic Inverse Property:   HOLDS

Al Property:   FAILS. The left inner mapping L1,1 = (2,5)(3,4)(6,9)(7,8) is not an automorphism.   L1,1(2*3) neq L1,1(2)*L1,1(3)

Ar Property:   HOLDS (i.e. every right inner mapping Ra,b is an automorphism)

Right (Left, Full) Mult Group Orders:   128 (18432, 36864)


/ revised November, 2001