Right Bol Loop 16.15.4.5 of order 16


0123456789101112131415
1032547698111015141312
2401673105118913121514
3510762114109814151213
4267015123151314810119
5376104152121413911108
6745230113141215108911
7654321014131512119810
8910111215131401234675
9811101512141310325764
1012891314112153016457
1115981413103122107546
1210131489154115670231
1314121510118967452013
1413151211109876543102
1511141398125104761320

Centre:   0

Centrum:   0   9   13   14

Nucleus:   0

Left Nucleus:   0   1   6   7   8   9   13   14

Middle Nucleus:   0

Right Nucleus:   0

1 Element of order 1:   0

15 Elements of order 2:   1   2   3   4   5   6   7   8   9   10   11   12   13   14   15

Commutator Subloop:   0   7   8   14

Associator Subloop:   0   7   8   14

1 Conjugacy Class of size 1:

1 Conjugacy Class of size 3:

3 Conjugacy Classes of size 4:

Automorphic Inverse Property:   HOLDS

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

Ar Property:   HOLDS (i.e. every right inner mapping Ra,b is an automorphism)

Right (Left, Full) Mult Group Orders:   64 (18432, 36864)


/ revised November, 2001