Element structure of groups of order 243: Difference between revisions

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Line 26: Line 26:
| || 9 || 1 || 26 || 216 || 0 || 0 || 0
| || 9 || 1 || 26 || 216 || 0 || 0 || 0
|-
|-
| ||10 || 1 || 8 || 72 || 162 || 0 || 0
| [[Direct product of Z27 and Z9]] ||10 || 1 || 8 || 72 || 162 || 0 || 0
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| ||11 || 1 || 8 || 72 || 162 || 0 || 0
| ||11 || 1 || 8 || 72 || 162 || 0 || 0
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| ||22 || 1 || 8 || 72 || 162 || 0 || 0
| ||22 || 1 || 8 || 72 || 162 || 0 || 0
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| ||23 || 1 || 8 || 18 || 54 || 162 || 0
| [[Direct product of Z81 and Z3]] ||23 || 1 || 8 || 18 || 54 || 162 || 0
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| ||24 || 1 || 8 || 18 || 54 || 162 || 0
| ||24 || 1 || 8 || 18 || 54 || 162 || 0
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| ||30 || 1 || 62 || 180 || 0 || 0 || 0
| ||30 || 1 || 62 || 180 || 0 || 0 || 0
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| ||31 || 1 || 26 || 216 || 0 || 0 || 0
| [[Direct product of Z9 and Z9 and Z3]] ||31 || 1 || 26 || 216 || 0 || 0 || 0
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| ||32 || 1 || 80 || 162 || 0 || 0 || 0
| ||32 || 1 || 80 || 162 || 0 || 0 || 0
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| ||47 || 1 || 26 || 216 || 0 || 0 || 0
| ||47 || 1 || 26 || 216 || 0 || 0 || 0
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| ||48 || 1 || 26 || 54 || 162 || 0 ||0
| [[Direct product of Z27 and E9]] ||48 || 1 || 26 || 54 || 162 || 0 ||0
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| ||49 || 1 || 26 || 54 || 162 || 0 || 0
| ||49 || 1 || 26 || 54 || 162 || 0 || 0
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| ||60 || 1 || 80 || 162|| 0 || 0 || 0
| ||60 || 1 || 80 || 162|| 0 || 0 || 0
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| ||61 || 1 || 80 || 162 || 0 || 0 || 0
| [[Direct product of Z9 and E27]] ||61 || 1 || 80 || 162 || 0 || 0 || 0
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| ||62 || 1 || 242 || 0 || 0 || 0 || 0
| ||62 || 1 || 242 || 0 || 0 || 0 || 0

Revision as of 01:50, 2 July 2010

Order statistics

FACTS TO CHECK AGAINST:

ORDER STATISTICS (cf. order statistics, order statistics-equivalent finite groups): number of nth roots is a multiple of n | Finite abelian groups with the same order statistics are isomorphic | Lazard Lie group has the same order statistics as the additive group of its Lazard Lie ring | Frobenius conjecture on nth roots

1-ISOMORPHISM (cf. 1-isomorphic groups): Lazard Lie group is 1-isomorphic to the additive group of its Lazard Lie ring | order statistics-equivalent not implies 1-isomorphic

Order statistics raw data

Group Second part of GAP ID Order 1 Order 3 Order 9 Order 27 Order 81 Order 243
Cyclic group:Z243 1 1 2 6 18 54 162
2 1 26 216 0 0 0
3 1 134 108 0 0 0
4 1 80 162 0 0 0
5 1 26 216 0 0 0
6 1 80 162 0 0 0
7 1 26 216 0 0 0
8 1 26 216 0 0 0
9 1 26 216 0 0 0
Direct product of Z27 and Z9 10 1 8 72 162 0 0
11 1 8 72 162 0 0
12 1 26 54 162 0 0
13 1 80 162 0 0 0
14 1 26 216 0 0 0
15 1 26 216 0 0 0
16 1 26 54 162 0 0
17 1 80 162 0 0 0
18 1 26 216 0 0 0
19 1 26 54 162 0 0
20 1 26 54 162 0 0
21 1 8 72 162 0 0
22 1 8 72 162 0 0
Direct product of Z81 and Z3 23 1 8 18 54 162 0
24 1 8 18 54 162 0
25 1 62 180 0 0 0
26 1 170 72 0 0 0
27 1 8 234 0 0 0
28 1 116 126 0 0 0
29 1 8 234 0 0 0
30 1 62 180 0 0 0
Direct product of Z9 and Z9 and Z3 31 1 26 216 0 0 0
32 1 80 162 0 0 0
33 1 26 216 0 0 0
34 1 26 216 0 0 0
35 1 80 162 0 0 0
36 1 26 216 0 0 0
37 1 242 0 0 0 0
38 1 80 162 0 0 0
39 1 80 162 0 0 0
40 1 80 162 0 0 0
41 1 26 216 0 0 0
42 1 26 216 0 0 0
43 1 26 216 0 0 0
44 1 26 216 0 0 0
45 1 26 216 0 0 0
46 1 26 216 0 0 0
47 1 26 216 0 0 0
Direct product of Z27 and E9 48 1 26 54 162 0 0
49 1 26 54 162 0 0
50 1 26 54 162 0 0
51 1 134 108 0 0 0
52 1 80 162 0 0 0
53 1 188 54 0 0 0
54 1 26 216 0 0 0
55 1 80 162 0 0 0
56 1 134 108 0 0 0
57 1 80 162 0 0 0
58 1 188 54 0 0 0
59 1 26 216 0 0 0
60 1 80 162 0 0 0
Direct product of Z9 and E27 61 1 80 162 0 0 0
62 1 242 0 0 0 0
63 1 80 162 0 0 0
64 1 80 162 0 0 0
65 1 242 0 0 0 0
66 1 80 162 0 0 0
Elementary abelian group:E243 1 242 0 0 0 0

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