Right Bol Loop 16.3.4.19 of order 16


0123456789101112131415
1230675491415108111213
2301547611109813121514
3012764510151491181312
4657203113118121514109
5746021312811131415910
6574310214121315910811
7465132015131214109118
8911101213141521305476
9111081514121336710245
1089111415131217632054
1110891312151403124567
1215131411891040256731
1314121581110952047613
1412151391081175461320
1513141210911864573102

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

3 Elements of order 2:   2   6   7

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

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)(8,11)(9,10)(12,13)(14,15) 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)(8,11)(9,12)(10,13)(14,15) 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