Right Bol Loop 16.11.4.1 of order 16


0123456789101112131415
1031071296248155141311
2451312711011415386109
3912015651141311210784
4213150814115121971063
5127680324109131111514
6101514301215111379248
7801112135121514643910
8711145415130112102936
9314121310115115046872
1061511191214130583427
1115471013289360145121
1256921103784140151113
1314829117410635150112
1413108615493721211105
1511943148106271131250

Centre:   0   5   14   15

Centrum:   0   5   14   15

Nucleus:   0   5   14   15

Left Nucleus:   0   2   5   7   9   10   14   15

Middle Nucleus:   0   5   14   15

Right Nucleus:   0   5   14   15

1 Element of order 1:   0

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

4 Elements of order 4:   2   7   9   10

Commutator Subloop:   0   5   14   15

Associator Subloop:   0   14

4 Conjugacy Classes of size 1:

3 Conjugacy Classes of size 4:

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