Right Bol Loop 16.11.2.45 of order 16


0123456789101112131415
1032765498111015141312
2301547610148121115913
3210674511139151012814
4756023113111591481210
5647201315121314910118
6574310212151413811109
7465132014101281391511
8121311101591406231475
9151410111281315320746
1014159813111223067514
1113128914101532154607
1281113149151060745321
1311812151014947513062
1410915121113874602153
1591014138121151476230

Centre:   0   5

Centrum:   0   5

Nucleus:   0   5

Left Nucleus:   0   1   5   6

Middle Nucleus:   0   5

Right Nucleus:   0   5


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   10   13   15

4 Elements of order 4:   9   11   12   14

Commutator Subloop:   0   5

Associator Subloop:   0   5

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

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

Al Property:   FAILS. The left inner mapping L1,8 = (10,13)(11,14) is not an automorphism.   L1,8(2*8) neq L1,8(2)*L1,8(8)

Ar Property:   HOLDS (i.e. every right inner mapping Ra,b is an automorphism)

Right (Left, Full) Mult Group Orders:   64 (1024, 2048)


/ revised October, 2001