Right Bol Loop 16.11.2.241 of order 16


0123456789101112131415
1230547691181015141312
2301765411109814151213
3012674510811913121514
4576013212131514111089
5764102313141215981011
6457320115121413101198
7645231014151312891110
8911101415131203127645
9111081514121310235467
1089111312141532016754
1110891213151421304576
1213141511109846570123
1314151210118954763210
1415121389101175642301
1512131498111067451032

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

11 Elements of order 2:   2   4   5   6   7   8   9   10   11   12   14

4 Elements of order 4:   1   3   13   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 = (8,11)(9,10) 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