Right Bol Loop 16.11.2.54 of order 16


0123456789101112131415
1230547691181013121514
2301765411109814151213
3012674510811915141312
4675013212131514119810
5467102313141215108911
6754320115121413911108
7546231014151312810119
8911101213151401327546
9111081312141512036457
1089111514121330215764
1110891415131223104675
1215141389101145670123
1312151498111057461032
1413121511109876542301
1514131210118964753210

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.


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:   128 (1024, 2048)


/ revised October, 2001