Right Bol Loop 16.7.2.391 of order 16


0123456789101112131415
1230547691181013121514
2301765411109815141312
3012674510811914151213
4675013212141315111098
5467102313121514101189
6754320114151213981110
7546231015131412891011
8101191514131223104567
9810111415121330215476
1011981312151412036745
1198101213141501327654
1213151411109875642310
1315141210118967453201
1412131598111054761023
1514121389101146570132

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   5   6   7   9   10

8 Elements of order 4:   1   3   8   11   12   13   14   15

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