Right Bol Loop 16.9.2.338 of order 16


0123456789101112131415
1121410111391502358467
2140111510121391476385
3151112914130104167258
4131514120109113285176
5111090121514137614832
6912131015011148532714
7101301491112155823641
8091513111410126741523
9284731560111014151213
1035826417110915141312
1143681725109013121514
1286754231141513011910
1357218364151412110109
1461537842121315910011
1574162583131214109110

Centre:   0   12

Centrum:   0   12

Nucleus:   0   12

Left Nucleus:   0   12

Middle Nucleus:   0   12

Right Nucleus:   0   12


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

9 Elements of order 2:   2   6   9   10   11   12   13   14   15

6 Elements of order 4:   1   3   4   5   7   8

Commutator Subloop:   0   12

Associator Subloop:   0   12

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

Automorphic Inverse Property:   FAILS.   (1-1)(3-1) neq (1*3)-1

Al Property:   FAILS. The left inner mapping L1,1 = (3,7)(10,15) 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 (1024, 2048)


/ revised October, 2001