Right Bol Loop 16.3.2.69 of order 16


0123456789101112131415
1230574691181014121513
2301765411109815141312
3012647510811913151214
4675213012141315810911
5467320113121514101189
6754102314151213981110
7546031215131412119108
8101191214131521304567
9810111312151432016475
1011981415121310235746
1198101513141203127654
1213151411109876540312
1315141210811964753201
1412131591181057461023
1514121389101145672130

Centre:   0   2

Centrum:   0   2

Nucleus:   0   2

Left Nucleus:   0   2   5   6

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

3 Elements of order 2:   2   12   15

12 Elements of order 4:   1   3   4   5   6   7   8   9   10   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:   FAILS.   (1-1)(5-1) neq (1*5)-1

Al Property:   FAILS. The left inner mapping L1,8 = (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:   64 (1024, 2048)


/ revised October, 2001