Right Bol Loop 16.3.4.3 of order 16


0123456789101112131415
1032548967111013121514
2310684105117915141213
3201865114109714151312
4579101331221514681011
5497011221331415861110
6811103215114013125479
7954131211501432111068
8610112314015112134597
9745121301411523101186
1011681514313212107945
1110861415212313019754
1213151479104115681023
1312141597115104860132
1415121310117698452301
1514131211109876543210

Centre:   0   1   14   15

Centrum:   0   1   14   15

Nucleus:   0   1   14   15

Left Nucleus:   0   1   4   5   10   11   14   15

Middle Nucleus:   0   1   14   15

Right Nucleus:   0   1   14   15

1 Element of order 1:   0

3 Elements of order 2:   1   14   15

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

Commutator Subloop:   0   1   14   15

Associator Subloop:   0   1

4 Conjugacy Classes of size 1:

3 Conjugacy Classes of size 4:

Automorphic Inverse Property:   FAILS.   (2-1)(5-1) neq (2*5)-1

Al Property:   HOLDS (i.e. every left inner mapping La,b is an automorphism)

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

Right (Left, Full) Mult Group Orders:   32 (64, 256)


/ revised October, 2001