Right Bol Loop 16.3.2.10 of order 16


0123456789101112131415
1250374691411101312158
2571063413101589141112
3014627510118151491213
4306715211129141581310
5762140312131498151011
6437502115813121110914
7645231014151213101189
8913101112151401543276
9131281014111517234560
1089111513141234760152
1110815149121345671023
1214151391181052017634
1312149815101123106745
1415111213109876325401
1511101412813960452317

Centre:   0   7

Centrum:   0   7

Nucleus:   0   7

Left Nucleus:   0   7

Middle Nucleus:   0   7

Right Nucleus:   0   7


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

3 Elements of order 2:   7   8   14

8 Elements of order 4:   2   4   9   10   11   12   13   15

4 Elements of order 8:   1   3   5   6

Commutator Subloop:   0   2   4   7

Associator Subloop:   0   2   4   7

2 Conjugacy Classes of size 1:

1 Conjugacy Class of size 2:

3 Conjugacy Classes of size 4:

Automorphic Inverse Property:   FAILS.   (1-1)(9-1) neq (1*9)-1

Al Property:   FAILS. The left inner mapping L1,1 = (8,13)(9,10)(11,14)(12,15) is not an automorphism.   L1,1(1*8) neq L1,1(1)*L1,1(8)

Ar Property:   FAILS. The right inner mapping R1,8 = (1,5)(2,4)(3,6)(9,12)(10,15)(11,13) is not an automorphism.   R1,8(1*9) neq R1,8(1)*R1,8(9)

Right (Left, Full) Mult Group Orders:   64 (4096, 16384)


/ revised October, 2001