Right Bol Loop 16.7.4.19 of order 16

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

Centre: 0 7

Centrum: 0 2 6 7

Nucleus: 0 7

Left Nucleus: 0 2 6 7

Middle Nucleus: 0 7

Right Nucleus: 0 7

Comm(L): This graph has as its 7 vertices the nontrivial cosets of the centre. Edges represent non-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 2 6 7

Associator Subloop: 0 2 6 7

2 Conjugacy Classes of size 1:

1 Conjugacy Class of size 2:

3 Conjugacy Classes of size 4:

1 3 4 5
8 10 14 15
9 11 12 13

Automorphic Inverse Property: FAILS. (1^-1)(9^-1) neq (1*9)^-1

A_l Property: FAILS. The left inner mapping L_1,8 = (2,6)(3,4)(8,10)(9,11)(12,13)(14,15) is not an automorphism. L_1,8(2*8) neq L_1,8(2)*L_1,8(8)

A_r Property: FAILS. The right inner mapping R_1,8 = (1,4)(3,5)(8,10)(9,12)(11,13)(14,15) is not an automorphism. R_1,8(8*1) neq R_1,8(8)*R_1,8(1)

Right (Left, Full) Mult Group Orders: 64 (4096, 16384)

/ revised October, 2001

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

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

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