Right Bol Loop 16.7.2.163 of order 16


0123456789101112131415
1230574698111014151213
2301765411109815141312
3012647510118913121514
4675013212131415119108
5467120314151213108119
6754302113121514911810
7546231015141312810911
8101191513141223107564
9810111312151432016475
1011981415121310235746
1198101214131501324657
1214151311109875640312
1312141591181057463021
1415131210811964751203
1513121489101146572130

Centre:   0   2

Centrum:   0   2

Nucleus:   0   2

Left Nucleus:   0   2

Middle Nucleus:   0   2

Right Nucleus:   0   2


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

7 Elements of order 2:   2   4   7   12   13   14   15

8 Elements of order 4:   1   3   5   6   8   9   10   11

Commutator Subloop:   0   2

Associator Subloop:   0   2

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 = (4,7)(5,6)(8,11)(9,10)(12,15)(13,14) is not an automorphism.   L1,8(4*8) neq L1,8(4)*L1,8(8)

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