Right Bol Loop 16.3.4.20 of order 16


0123456789101112131415
1230764591514108111312
2301547611109813121514
3012675410141591181213
4756201312811131514109
5647023113118121415910
6475130215121314910118
7564312014131215109811
8911101312151423105467
9111081514121337612045
1089111415131216730254
1110891213141501324576
1214131581191052047613
1315121411810940256731
1413151291011864571320
1512141310981175463102

Centre:   0   2

Centrum:   0   2   6   7

Nucleus:   0   2

Left Nucleus:   0   2   6   7

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

3 Elements of order 2:   2   6   7

12 Elements of order 4:   1   3   4   5   8   9   10   11   12   13   14   15

Commutator Subloop:   0   2   6   7

Associator Subloop:   0   2   6   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 L1,8 = (4,5)(6,7) is not an automorphism.   L1,8(4*8) neq L1,8(4)*L1,8(8)

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

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


/ revised October, 2001