Right Bol Loop 16.11.2.65 of order 16


0123456789101112131415
1230547691181015141312
2301765411109814151213
3012674510811913121514
4675013212131514119810
5467102313141215911108
6754320115121413108911
7546231014151312810119
8911101413151201327645
9111081512141312035467
1089111314121530216754
1110891215131423104576
1215141311910845670321
1312151410811957463012
1413121581091176542103
1514131291181064751230

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 = (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