Right Bol Loop 16.7.4.17 of order 16


0123456789101112131415
1230675491514101181213
2301547611109813121514
3012764510141598111312
4657203112118131514910
5746021313811121415109
6574310215131214109118
7465132014121315910811
8101191213151403125476
9810111514131217630245
1011981415121336712054
1198101312141521304567
1214131511810940257613
1315121481191052046731
1413151291011875463102
1512141310981164571320

Centre:   0   2

Centrum:   0   2   6   7

Nucleus:   0   2

Left Nucleus:   0   2   6   7

Middle Nucleus:   0   2

Right Nucleus:   0   2


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:   2   6   7   8   11   14   15

8 Elements of order 4:   1   3   4   5   9   10   12   13

Commutator Subloop:   0   2   6   7

Associator Subloop:   0   2   6   7

2 Conjugacy Classes of size 1:

1 Conjugacy Class of size 2:

3 Conjugacy Classes of size 4:

Automorphic Inverse Property:   FAILS.   (1-1)(9-1) neq (1*9)-1

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

Ar Property:   FAILS. The right inner mapping R1,8 = (1,4)(3,5)(9,12)(10,13) is not an automorphism.   R1,8(8*1) neq R1,8(8)*R1,8(1)

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


/ revised October, 2001