Right Bol Loop 30.1.2.0 of order 30

0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27	28	29
1	2	4	0	3	6	9	5	7	8	11	13	10	14	12	16	19	15	17	18	23	20	25	26	29	28	27	21	24	22
2	4	3	1	0	9	8	6	5	7	13	14	11	12	10	19	18	16	15	17	26	23	28	27	22	24	21	20	29	25
3	0	1	4	2	7	5	8	9	6	12	10	14	11	13	17	15	18	19	16	21	27	29	20	28	22	23	26	25	24
4	3	0	2	1	8	7	9	6	5	14	12	13	10	11	18	17	19	16	15	27	26	24	21	25	29	20	23	22	28
5	6	9	7	8	10	13	14	11	12	0	4	2	1	3	20	23	21	27	26	24	25	16	22	15	17	28	29	19	18
6	9	8	5	7	11	14	12	13	10	1	3	4	2	0	23	26	20	21	27	29	28	19	25	16	15	24	22	18	17
7	5	6	8	9	12	11	13	10	14	3	2	1	0	4	21	20	27	26	23	28	22	15	29	17	18	25	24	16	19
8	7	5	9	6	14	10	11	12	13	4	1	0	3	2	27	21	26	23	20	25	29	17	24	18	19	22	28	15	16
9	8	7	6	5	13	12	10	14	11	2	0	3	4	1	26	27	23	20	21	22	24	18	28	19	16	29	25	17	15
10	14	11	13	12	0	2	4	1	3	5	6	7	9	8	29	28	25	24	22	16	17	27	18	23	21	15	19	20	26
11	12	13	14	10	1	4	3	2	0	6	9	5	8	7	22	24	28	29	25	19	15	21	17	26	20	16	18	23	27
12	13	10	11	14	3	1	2	0	4	7	5	8	6	9	24	25	22	28	29	15	18	26	19	20	27	17	16	21	23
13	10	14	12	11	2	3	0	4	1	9	8	6	7	5	25	29	24	22	28	18	16	20	15	27	23	19	17	26	21
14	11	12	10	13	4	0	1	3	2	8	7	9	5	6	28	22	29	25	24	17	19	23	16	21	26	18	15	27	20
15	16	19	17	18	20	23	21	27	26	28	24	25	29	22	2	4	1	0	3	9	6	10	8	14	11	7	5	13	12
16	19	18	15	17	23	26	20	21	27	24	29	28	22	25	4	3	2	1	0	8	9	11	7	12	13	5	6	14	10
17	15	16	18	19	21	20	27	26	23	25	28	22	24	29	1	2	0	3	4	6	5	12	9	13	10	8	7	11	14
18	17	15	19	16	27	21	26	23	20	22	25	29	28	24	0	1	3	4	2	5	7	14	6	11	12	9	8	10	13
19	18	17	16	15	26	27	23	20	21	29	22	24	25	28	3	0	4	2	1	7	8	13	5	10	14	6	9	12	11
20	23	26	21	27	28	29	22	24	25	15	18	19	16	17	9	8	6	5	7	14	11	4	10	2	1	13	12	3	0
21	20	23	27	26	25	24	29	28	22	17	19	16	15	18	6	9	5	7	8	13	10	2	12	1	0	11	14	4	3
22	24	25	28	29	18	15	16	17	19	27	21	26	20	23	13	10	12	11	14	1	3	8	4	6	7	0	2	5	9
23	26	27	20	21	24	22	25	29	28	16	17	18	19	15	8	7	9	6	5	12	13	3	11	4	2	14	10	0	1
24	25	29	22	28	16	18	17	19	15	23	26	20	27	21	10	14	13	12	11	3	2	6	1	7	9	4	0	8	5
25	29	28	24	22	17	16	19	15	18	21	20	27	23	26	14	11	10	13	12	2	0	7	3	9	5	1	4	6	8
26	27	21	23	20	29	25	28	22	24	19	15	17	18	16	7	5	8	9	6	10	14	0	13	3	4	12	11	1	2
27	21	20	26	23	22	28	24	25	29	18	16	15	17	19	5	6	7	8	9	11	12	1	14	0	3	10	13	2	4
28	22	24	29	25	15	19	18	16	17	20	23	21	26	27	12	13	11	14	10	4	1	5	0	8	6	2	3	9	7
29	28	22	25	24	19	17	15	18	16	26	27	23	21	20	11	12	14	10	13	0	4	9	2	5	8	3	1	7	6

Centre: 0 17

Centrum: 0 17

Nucleus: 0 17

Left Nucleus: 0 1 2 3 4 15 16 17 18 19

Middle Nucleus: 0 17

Right Nucleus: 0 17

1 Element of order 1: 0

1 Element of order 2: 17

10 Elements of order 3: 5 6 7 8 9 10 11 12 13 14

4 Elements of order 5: 1 2 3 4

10 Elements of order 6: 20 21 22 23 24 25 26 27 28 29

4 Elements of order 10: 15 16 18 19

Commutator Subloop: 0 1 2 3 4

Associator Subloop: 0 1 2 3 4

2 Conjugacy Classes of size 1:

2 Conjugacy Classes of size 4:

1 2 3 4
15 16 18 19

4 Conjugacy Classes of size 5:

5 6 7 8 9
10 11 12 13 14
20 21 23 26 27
22 24 25 28 29

Automorphic Inverse Property: FAILS. (1^-1)(6^-1) neq (1*6)^-1

A_l Property: FAILS. The left inner mapping L_1,10 = (5,9,7,6,8)(10,14,11,12,13)(20,26,21,23,27)(22,24,25,29,28) is not an automorphism. L_1,10(5*5) neq L_1,10(5)*L_1,10(5)

A_r Property: FAILS. The right inner mapping R_1,5 = (5,7,8,9,6)(10,11,13,14,12)(20,21,27,26,23)(22,25,28,24,29) is not an automorphism. R_1,5(5*5) neq R_1,5(5)*R_1,5(5)

Right (Left, Full) Mult Group Orders: 150 (12000, 12000)

/ revised November, 2001

0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27	28	29
1	2	4	0	3	6	9	5	7	8	11	13	10	14	12	16	19	15	17	18	23	20	25	26	29	28	27	21	24	22
2	4	3	1	0	9	8	6	5	7	13	14	11	12	10	19	18	16	15	17	26	23	28	27	22	24	21	20	29	25
3	0	1	4	2	7	5	8	9	6	12	10	14	11	13	17	15	18	19	16	21	27	29	20	28	22	23	26	25	24
4	3	0	2	1	8	7	9	6	5	14	12	13	10	11	18	17	19	16	15	27	26	24	21	25	29	20	23	22	28
5	6	9	7	8	10	13	14	11	12	0	4	2	1	3	20	23	21	27	26	24	25	16	22	15	17	28	29	19	18
6	9	8	5	7	11	14	12	13	10	1	3	4	2	0	23	26	20	21	27	29	28	19	25	16	15	24	22	18	17
7	5	6	8	9	12	11	13	10	14	3	2	1	0	4	21	20	27	26	23	28	22	15	29	17	18	25	24	16	19
8	7	5	9	6	14	10	11	12	13	4	1	0	3	2	27	21	26	23	20	25	29	17	24	18	19	22	28	15	16
9	8	7	6	5	13	12	10	14	11	2	0	3	4	1	26	27	23	20	21	22	24	18	28	19	16	29	25	17	15
10	14	11	13	12	0	2	4	1	3	5	6	7	9	8	29	28	25	24	22	16	17	27	18	23	21	15	19	20	26
11	12	13	14	10	1	4	3	2	0	6	9	5	8	7	22	24	28	29	25	19	15	21	17	26	20	16	18	23	27
12	13	10	11	14	3	1	2	0	4	7	5	8	6	9	24	25	22	28	29	15	18	26	19	20	27	17	16	21	23
13	10	14	12	11	2	3	0	4	1	9	8	6	7	5	25	29	24	22	28	18	16	20	15	27	23	19	17	26	21
14	11	12	10	13	4	0	1	3	2	8	7	9	5	6	28	22	29	25	24	17	19	23	16	21	26	18	15	27	20
15	16	19	17	18	20	23	21	27	26	28	24	25	29	22	2	4	1	0	3	9	6	10	8	14	11	7	5	13	12
16	19	18	15	17	23	26	20	21	27	24	29	28	22	25	4	3	2	1	0	8	9	11	7	12	13	5	6	14	10
17	15	16	18	19	21	20	27	26	23	25	28	22	24	29	1	2	0	3	4	6	5	12	9	13	10	8	7	11	14
18	17	15	19	16	27	21	26	23	20	22	25	29	28	24	0	1	3	4	2	5	7	14	6	11	12	9	8	10	13
19	18	17	16	15	26	27	23	20	21	29	22	24	25	28	3	0	4	2	1	7	8	13	5	10	14	6	9	12	11
20	23	26	21	27	28	29	22	24	25	15	18	19	16	17	9	8	6	5	7	14	11	4	10	2	1	13	12	3	0
21	20	23	27	26	25	24	29	28	22	17	19	16	15	18	6	9	5	7	8	13	10	2	12	1	0	11	14	4	3
22	24	25	28	29	18	15	16	17	19	27	21	26	20	23	13	10	12	11	14	1	3	8	4	6	7	0	2	5	9
23	26	27	20	21	24	22	25	29	28	16	17	18	19	15	8	7	9	6	5	12	13	3	11	4	2	14	10	0	1
24	25	29	22	28	16	18	17	19	15	23	26	20	27	21	10	14	13	12	11	3	2	6	1	7	9	4	0	8	5
25	29	28	24	22	17	16	19	15	18	21	20	27	23	26	14	11	10	13	12	2	0	7	3	9	5	1	4	6	8
26	27	21	23	20	29	25	28	22	24	19	15	17	18	16	7	5	8	9	6	10	14	0	13	3	4	12	11	1	2
27	21	20	26	23	22	28	24	25	29	18	16	15	17	19	5	6	7	8	9	11	12	1	14	0	3	10	13	2	4
28	22	24	29	25	15	19	18	16	17	20	23	21	26	27	12	13	11	14	10	4	1	5	0	8	6	2	3	9	7
29	28	22	25	24	19	17	15	18	16	26	27	23	21	20	11	12	14	10	13	0	4	9	2	5	8	3	1	7	6

0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27	28	29
1	2	4	0	3	6	9	5	7	8	11	13	10	14	12	16	19	15	17	18	23	20	25	26	29	28	27	21	24	22
2	4	3	1	0	9	8	6	5	7	13	14	11	12	10	19	18	16	15	17	26	23	28	27	22	24	21	20	29	25
3	0	1	4	2	7	5	8	9	6	12	10	14	11	13	17	15	18	19	16	21	27	29	20	28	22	23	26	25	24
4	3	0	2	1	8	7	9	6	5	14	12	13	10	11	18	17	19	16	15	27	26	24	21	25	29	20	23	22	28
5	6	9	7	8	10	13	14	11	12	0	4	2	1	3	20	23	21	27	26	24	25	16	22	15	17	28	29	19	18
6	9	8	5	7	11	14	12	13	10	1	3	4	2	0	23	26	20	21	27	29	28	19	25	16	15	24	22	18	17
7	5	6	8	9	12	11	13	10	14	3	2	1	0	4	21	20	27	26	23	28	22	15	29	17	18	25	24	16	19
8	7	5	9	6	14	10	11	12	13	4	1	0	3	2	27	21	26	23	20	25	29	17	24	18	19	22	28	15	16
9	8	7	6	5	13	12	10	14	11	2	0	3	4	1	26	27	23	20	21	22	24	18	28	19	16	29	25	17	15
10	14	11	13	12	0	2	4	1	3	5	6	7	9	8	29	28	25	24	22	16	17	27	18	23	21	15	19	20	26
11	12	13	14	10	1	4	3	2	0	6	9	5	8	7	22	24	28	29	25	19	15	21	17	26	20	16	18	23	27
12	13	10	11	14	3	1	2	0	4	7	5	8	6	9	24	25	22	28	29	15	18	26	19	20	27	17	16	21	23
13	10	14	12	11	2	3	0	4	1	9	8	6	7	5	25	29	24	22	28	18	16	20	15	27	23	19	17	26	21
14	11	12	10	13	4	0	1	3	2	8	7	9	5	6	28	22	29	25	24	17	19	23	16	21	26	18	15	27	20
15	16	19	17	18	20	23	21	27	26	28	24	25	29	22	2	4	1	0	3	9	6	10	8	14	11	7	5	13	12
16	19	18	15	17	23	26	20	21	27	24	29	28	22	25	4	3	2	1	0	8	9	11	7	12	13	5	6	14	10
17	15	16	18	19	21	20	27	26	23	25	28	22	24	29	1	2	0	3	4	6	5	12	9	13	10	8	7	11	14
18	17	15	19	16	27	21	26	23	20	22	25	29	28	24	0	1	3	4	2	5	7	14	6	11	12	9	8	10	13
19	18	17	16	15	26	27	23	20	21	29	22	24	25	28	3	0	4	2	1	7	8	13	5	10	14	6	9	12	11
20	23	26	21	27	28	29	22	24	25	15	18	19	16	17	9	8	6	5	7	14	11	4	10	2	1	13	12	3	0
21	20	23	27	26	25	24	29	28	22	17	19	16	15	18	6	9	5	7	8	13	10	2	12	1	0	11	14	4	3
22	24	25	28	29	18	15	16	17	19	27	21	26	20	23	13	10	12	11	14	1	3	8	4	6	7	0	2	5	9
23	26	27	20	21	24	22	25	29	28	16	17	18	19	15	8	7	9	6	5	12	13	3	11	4	2	14	10	0	1
24	25	29	22	28	16	18	17	19	15	23	26	20	27	21	10	14	13	12	11	3	2	6	1	7	9	4	0	8	5
25	29	28	24	22	17	16	19	15	18	21	20	27	23	26	14	11	10	13	12	2	0	7	3	9	5	1	4	6	8
26	27	21	23	20	29	25	28	22	24	19	15	17	18	16	7	5	8	9	6	10	14	0	13	3	4	12	11	1	2
27	21	20	26	23	22	28	24	25	29	18	16	15	17	19	5	6	7	8	9	11	12	1	14	0	3	10	13	2	4
28	22	24	29	25	15	19	18	16	17	20	23	21	26	27	12	13	11	14	10	4	1	5	0	8	6	2	3	9	7
29	28	22	25	24	19	17	15	18	16	26	27	23	21	20	11	12	14	10	13	0	4	9	2	5	8	3	1	7	6

0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27	28	29
1	2	4	0	3	6	9	5	7	8	11	13	10	14	12	16	19	15	17	18	23	20	25	26	29	28	27	21	24	22
2	4	3	1	0	9	8	6	5	7	13	14	11	12	10	19	18	16	15	17	26	23	28	27	22	24	21	20	29	25
3	0	1	4	2	7	5	8	9	6	12	10	14	11	13	17	15	18	19	16	21	27	29	20	28	22	23	26	25	24
4	3	0	2	1	8	7	9	6	5	14	12	13	10	11	18	17	19	16	15	27	26	24	21	25	29	20	23	22	28
5	6	9	7	8	10	13	14	11	12	0	4	2	1	3	20	23	21	27	26	24	25	16	22	15	17	28	29	19	18
6	9	8	5	7	11	14	12	13	10	1	3	4	2	0	23	26	20	21	27	29	28	19	25	16	15	24	22	18	17
7	5	6	8	9	12	11	13	10	14	3	2	1	0	4	21	20	27	26	23	28	22	15	29	17	18	25	24	16	19
8	7	5	9	6	14	10	11	12	13	4	1	0	3	2	27	21	26	23	20	25	29	17	24	18	19	22	28	15	16
9	8	7	6	5	13	12	10	14	11	2	0	3	4	1	26	27	23	20	21	22	24	18	28	19	16	29	25	17	15
10	14	11	13	12	0	2	4	1	3	5	6	7	9	8	29	28	25	24	22	16	17	27	18	23	21	15	19	20	26
11	12	13	14	10	1	4	3	2	0	6	9	5	8	7	22	24	28	29	25	19	15	21	17	26	20	16	18	23	27
12	13	10	11	14	3	1	2	0	4	7	5	8	6	9	24	25	22	28	29	15	18	26	19	20	27	17	16	21	23
13	10	14	12	11	2	3	0	4	1	9	8	6	7	5	25	29	24	22	28	18	16	20	15	27	23	19	17	26	21
14	11	12	10	13	4	0	1	3	2	8	7	9	5	6	28	22	29	25	24	17	19	23	16	21	26	18	15	27	20
15	16	19	17	18	20	23	21	27	26	28	24	25	29	22	2	4	1	0	3	9	6	10	8	14	11	7	5	13	12
16	19	18	15	17	23	26	20	21	27	24	29	28	22	25	4	3	2	1	0	8	9	11	7	12	13	5	6	14	10
17	15	16	18	19	21	20	27	26	23	25	28	22	24	29	1	2	0	3	4	6	5	12	9	13	10	8	7	11	14
18	17	15	19	16	27	21	26	23	20	22	25	29	28	24	0	1	3	4	2	5	7	14	6	11	12	9	8	10	13
19	18	17	16	15	26	27	23	20	21	29	22	24	25	28	3	0	4	2	1	7	8	13	5	10	14	6	9	12	11
20	23	26	21	27	28	29	22	24	25	15	18	19	16	17	9	8	6	5	7	14	11	4	10	2	1	13	12	3	0
21	20	23	27	26	25	24	29	28	22	17	19	16	15	18	6	9	5	7	8	13	10	2	12	1	0	11	14	4	3
22	24	25	28	29	18	15	16	17	19	27	21	26	20	23	13	10	12	11	14	1	3	8	4	6	7	0	2	5	9
23	26	27	20	21	24	22	25	29	28	16	17	18	19	15	8	7	9	6	5	12	13	3	11	4	2	14	10	0	1
24	25	29	22	28	16	18	17	19	15	23	26	20	27	21	10	14	13	12	11	3	2	6	1	7	9	4	0	8	5
25	29	28	24	22	17	16	19	15	18	21	20	27	23	26	14	11	10	13	12	2	0	7	3	9	5	1	4	6	8
26	27	21	23	20	29	25	28	22	24	19	15	17	18	16	7	5	8	9	6	10	14	0	13	3	4	12	11	1	2
27	21	20	26	23	22	28	24	25	29	18	16	15	17	19	5	6	7	8	9	11	12	1	14	0	3	10	13	2	4
28	22	24	29	25	15	19	18	16	17	20	23	21	26	27	12	13	11	14	10	4	1	5	0	8	6	2	3	9	7
29	28	22	25	24	19	17	15	18	16	26	27	23	21	20	11	12	14	10	13	0	4	9	2	5	8	3	1	7	6