Right Bol Loop 16.7.2.256 of order 16


0123456789101112131415
1230574698111014151213
2301765411109815141312
3012647510118913121514
4675031212131415891011
5467102314151213981110
6754320113121514101189
7546213015141312111098
8101191513141223104657
9810111312151432015746
1011981415121310236475
1198101214131501327564
1214151311910875640132
1312141598111057463201
1415131210118964751023
1513121481091146572310

Centre:   0   2

Centrum:   0   2

Nucleus:   0   2

Left Nucleus:   0   2   4   7

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   4   5   6   7   12   15

8 Elements of order 4:   1   3   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 = (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:   64 (1024, 2048)


/ revised October, 2001