Right Bol Loop 16.11.4.4 of order 16


0123456789101112131415
1032674591415108111213
2301765410151491181312
3210547611109813121514
4675031212811131415910
5764302113118121514109
6457120314121315910811
7546213015131214109118
8912111013141501234567
9814101115121316720345
1011159814131227613054
1110138912151432105476
1214813151191040356712
1315111214810953047621
1412915131081164571203
1513101412911875462130

Centre:   0   7

Centrum:   0   3   6   7

Nucleus:   0   7

Left Nucleus:   0   3   6   7

Middle Nucleus:   0   7

Right Nucleus:   0   7


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

11 Elements of order 2:   1   2   3   4   5   6   7   8   11   14   15

4 Elements of order 4:   9   10   12   13

Commutator Subloop:   0   3   6   7

Associator Subloop:   0   3   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 = (2,4)(3,6) is not an automorphism.   L1,8(2*8) neq L1,8(2)*L1,8(8)

Ar Property:   FAILS. The right inner mapping R1,8 = (1,4)(2,5)(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