Right Bol Loop 16.11.2.155 of order 16


0123456789101112131415
1230574691181013141512
2301765411109814151213
3012647510811915121314
4675031212131514111089
5467102313141215108911
6754320115121413911108
7546213014151312891110
8911101415131201327546
9111081512141312036754
1089111314121530215467
1110891213151423104675
1215141311910845670321
1312151410118957461032
1413121581091176542103
1514131298111064753210

Centre:   0   2

Centrum:   0   2

Nucleus:   0   2

Left Nucleus:   0   1   2   3

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   11   12   13   14   15

4 Elements of order 4:   1   3   9   10

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 = (12,14)(13,15) 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