Right Bol Loop 16.9.2.73 of order 16


0123456789101112131415
1151410121190136354827
2141512131009117438516
3131201491110154126758
4121314150101193271685
5111090151312148617234
6901110131514121583472
7091311121415102845361
8101115914121305762143
9215387640111310121514
1034126587120149151113
1143617852139015141012
1258271346101415091311
1385762431111591401210
1467483125151210131109
1576854213141312111090

Centre:   0   15

Centrum:   0   15

Nucleus:   0   15

Left Nucleus:   0   15

Middle Nucleus:   0   15

Right Nucleus:   0   15


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:   3   8   9   10   11   12   13   14   15

6 Elements of order 4:   1   2   4   5   6   7

Commutator Subloop:   0   15

Associator Subloop:   0   15

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

Automorphic Inverse Property:   FAILS.   (1-1)(4-1) neq (1*4)-1

Al Property:   FAILS. The left inner mapping L1,1 = (2,6)(3,8)(4,5)(9,14)(10,13)(11,12) 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