Right Bol Loop 16.7.2.432 of order 16

0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
1	0	3	2	7	6	5	4	9	15	11	12	13	10	8	14
2	3	0	1	5	4	7	6	10	13	15	9	8	14	11	12
3	2	1	0	6	7	4	5	11	10	14	15	9	8	12	13
4	7	5	6	0	2	3	1	15	14	12	13	10	11	9	8
5	6	4	7	2	0	1	3	12	11	8	14	15	9	13	10
6	5	7	4	3	1	0	2	13	12	9	8	14	15	10	11
7	4	6	5	1	3	2	0	14	8	13	10	11	12	15	9
8	9	12	13	15	10	11	14	4	1	2	3	5	6	7	0
9	8	13	12	14	11	10	15	7	4	3	5	6	2	0	1
10	11	15	14	12	8	9	13	5	6	4	1	0	7	3	2
11	10	14	15	13	9	8	12	6	2	7	4	1	0	5	3
12	13	8	9	10	15	14	11	2	3	0	7	4	1	6	5
13	12	9	8	11	14	15	10	3	5	1	0	7	4	2	6
14	15	11	10	9	13	12	8	1	0	6	2	3	5	4	7
15	14	10	11	8	12	13	9	0	7	5	6	2	3	1	4

Centre: 0 4

Centrum: 0 4

Nucleus: 0 4

Left Nucleus: 0 4

Middle Nucleus: 0 4

Right Nucleus: 0 4

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: 1 2 3 4 5 6 7

8 Elements of order 4: 8 9 10 11 12 13 14 15

Commutator Subloop: 0 4

Associator Subloop: 0 4

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

1 7
2 5
3 6
8 15
9 14
10 12
11 13

Automorphic Inverse Property: HOLDS

A_l Property: FAILS. The left inner mapping L_1,8 = (8,15)(9,14) is not an automorphism. L_1,8(2*8) neq L_1,8(2)*L_1,8(8)

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

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

/ revised October, 2001

0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
1	0	3	2	7	6	5	4	9	15	11	12	13	10	8	14
2	3	0	1	5	4	7	6	10	13	15	9	8	14	11	12
3	2	1	0	6	7	4	5	11	10	14	15	9	8	12	13
4	7	5	6	0	2	3	1	15	14	12	13	10	11	9	8
5	6	4	7	2	0	1	3	12	11	8	14	15	9	13	10
6	5	7	4	3	1	0	2	13	12	9	8	14	15	10	11
7	4	6	5	1	3	2	0	14	8	13	10	11	12	15	9
8	9	12	13	15	10	11	14	4	1	2	3	5	6	7	0
9	8	13	12	14	11	10	15	7	4	3	5	6	2	0	1
10	11	15	14	12	8	9	13	5	6	4	1	0	7	3	2
11	10	14	15	13	9	8	12	6	2	7	4	1	0	5	3
12	13	8	9	10	15	14	11	2	3	0	7	4	1	6	5
13	12	9	8	11	14	15	10	3	5	1	0	7	4	2	6
14	15	11	10	9	13	12	8	1	0	6	2	3	5	4	7
15	14	10	11	8	12	13	9	0	7	5	6	2	3	1	4

0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
1	0	3	2	7	6	5	4	9	15	11	12	13	10	8	14
2	3	0	1	5	4	7	6	10	13	15	9	8	14	11	12
3	2	1	0	6	7	4	5	11	10	14	15	9	8	12	13
4	7	5	6	0	2	3	1	15	14	12	13	10	11	9	8
5	6	4	7	2	0	1	3	12	11	8	14	15	9	13	10
6	5	7	4	3	1	0	2	13	12	9	8	14	15	10	11
7	4	6	5	1	3	2	0	14	8	13	10	11	12	15	9
8	9	12	13	15	10	11	14	4	1	2	3	5	6	7	0
9	8	13	12	14	11	10	15	7	4	3	5	6	2	0	1
10	11	15	14	12	8	9	13	5	6	4	1	0	7	3	2
11	10	14	15	13	9	8	12	6	2	7	4	1	0	5	3
12	13	8	9	10	15	14	11	2	3	0	7	4	1	6	5
13	12	9	8	11	14	15	10	3	5	1	0	7	4	2	6
14	15	11	10	9	13	12	8	1	0	6	2	3	5	4	7
15	14	10	11	8	12	13	9	0	7	5	6	2	3	1	4

0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
1	0	3	2	7	6	5	4	9	15	11	12	13	10	8	14
2	3	0	1	5	4	7	6	10	13	15	9	8	14	11	12
3	2	1	0	6	7	4	5	11	10	14	15	9	8	12	13
4	7	5	6	0	2	3	1	15	14	12	13	10	11	9	8
5	6	4	7	2	0	1	3	12	11	8	14	15	9	13	10
6	5	7	4	3	1	0	2	13	12	9	8	14	15	10	11
7	4	6	5	1	3	2	0	14	8	13	10	11	12	15	9
8	9	12	13	15	10	11	14	4	1	2	3	5	6	7	0
9	8	13	12	14	11	10	15	7	4	3	5	6	2	0	1
10	11	15	14	12	8	9	13	5	6	4	1	0	7	3	2
11	10	14	15	13	9	8	12	6	2	7	4	1	0	5	3
12	13	8	9	10	15	14	11	2	3	0	7	4	1	6	5
13	12	9	8	11	14	15	10	3	5	1	0	7	4	2	6
14	15	11	10	9	13	12	8	1	0	6	2	3	5	4	7
15	14	10	11	8	12	13	9	0	7	5	6	2	3	1	4