Right Bol Loop 16.7.2.425 of order 16


0123456789101112131415
1230547691181013121514
2301765411109814151213
3012674510811915141312
4675213012131514891110
5467302115121413101198
6754120313141215981011
7546031214151312111089
8911101413151201327645
9111081314121512035467
1089111512141330216754
1110891215131423104576
1213141581091146572103
1314151210811967453012
1415121311910875640321
1512131491181054761230

Centre:   0   2

Centrum:   0   2

Nucleus:   0   2

Left Nucleus:   0   2

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. Here we print (in reverse video) the complementary graph, in which edges represent commuting cosets.


1 Element of order 1:   0

7 Elements of order 2:   2   5   6   8   11   13   15

8 Elements of order 4:   1   3   4   7   9   10   12   14

Commutator Subloop:   0   2

Associator Subloop:   0   2

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

Automorphic Inverse Property:   HOLDS

Al Property:   FAILS. The left inner mapping L1,8 = (12,14)(13,15) is not an automorphism.   L1,8(4*8) neq L1,8(4)*L1,8(8)

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

Right (Left, Full) Mult Group Orders:   128 (1024, 2048)


/ revised October, 2001