Right Bol Loop 16.7.2.375 of order 16


0123456789101112131415
1230547698111014121513
2301765411109815141312
3012674510118913151214
4675213012131415111098
5467302113121514911810
6754120314151213108119
7546031215141312891011
8101191514131221307564
9810111415121330215476
1011981312151412036745
1198101213141503124657
1213151481091175640312
1315141291181064753201
1412131510811957461023
1514121311910846572130

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. Here we print (in reverse video) the complementary graph, in which edges represent commuting cosets.


1 Element of order 1:   0

7 Elements of order 2:   2   5   6   9   10   12   15

8 Elements of order 4:   1   3   4   7   8   11   13   14

Commutator Subloop:   0   2

Associator Subloop:   0   2

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

Automorphic Inverse Property:   HOLDS

Al Property:   FAILS. The left inner mapping L1,8 = (4,7)(5,6) 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