Right Bol Loop 16.5.4.25 of order 16


0123456789101112131415
1121514131110902358467
2151211101413091467358
3141309151211104826715
4131415120910113715826
5111090121514136284173
6101112159013145173284
7901314101112158532641
8091011131415127641532
9215634870111015141312
1034872156111215149013
1143218765101512130914
1287654321151413011109
1356781234149011121510
1465127843130910151211
1578436512121314910110

Centre:   0   12

Centrum:   0   10   12   14

Nucleus:   0   12

Left Nucleus:   0   10   12   14

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

5 Elements of order 2:   3   6   9   12   15

10 Elements of order 4:   1   2   4   5   7   8   10   11   13   14

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)(5-1) neq (1*5)-1

Al Property:   FAILS. The left inner mapping L1,1 = (4,5)(11,13) 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:   64 (1024, 2048)


/ revised October, 2001