Right Bol Loop 16.7.2.428 of order 16


0123456789101112131415
1032574698111014121513
2301647510118913151214
3210765411109815141312
4657021312131415111098
5746103213121514911810
6475230114151213108119
7564312015141312891011
8910111513141232104567
9811101415121323016475
1011891312151410325746
1110981214131501237654
1214131511109876543210
1315121410811967451302
1412151391181054762031
1513141289101145670123

Centre:   0   3

Centrum:   0   3

Nucleus:   0   3

Left Nucleus:   0   3

Middle Nucleus:   0   3

Right Nucleus:   0   3


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:   1   2   3   4   5   6   7

8 Elements of order 4:   8   9   10   11   12   13   14   15

Commutator Subloop:   0   3

Associator Subloop:   0   3

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