Right Bol Loop 16.11.2.269 of order 16


0123456789101112131415
1036725131011891514412
2309181210547614151113
3211012111586141354097
4149121008157251331116
5615110101927431312814
6512815901131314271104
7131015811104521469123
8101314274301211596511
9114761413512015182310
1087135414211501211369
1191443137615112010528
1215651332149811100471
1378011129114634510152
1441119151012133672805
1512521463411109817130

Centre:   0

Centrum:   0   10

Nucleus:   0

Left Nucleus:   0   10   11   12

Middle Nucleus:   0

Right Nucleus:   0

1 Element of order 1:   0

11 Elements of order 2:   1   2   6   7   8   9   10   11   12   14   15

4 Elements of order 4:   3   4   5   13

Commutator Subloop:   0   10   11   12

Associator Subloop:   0   10   11   12

1 Conjugacy Class of size 1:

1 Conjugacy Class of size 3:

3 Conjugacy Classes of size 4:

Automorphic Inverse Property:   FAILS.   (1-1)(3-1) neq (1*3)-1

Al Property:   FAILS. The left inner mapping L1,2 = (2,14)(3,4)(5,13)(6,7)(8,15,9)(10,11,12) is not an automorphism.   L1,2(1*8) neq L1,2(1)*L1,2(8)

Ar Property:   FAILS. The right inner mapping R1,2 = (1,15)(2,14)(3,13)(4,5)(6,7)(8,9) is not an automorphism.   R1,2(2*1) neq R1,2(2)*R1,2(1)

Right (Left, Full) Mult Group Orders:   128 (18432, 36864)


/ revised November, 2001