Groups of order 81: Difference between revisions
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{{groups of order|81}} | {{groups of order|81}} | ||
This article gives basic information comparing and contrasting groups of order <math>81</math>. See also more detailed information on specific subtopics through the links: | |||
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! Information type !! Page summarizing information for groups of order 81 | |||
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| element structure || [[element structure of groups of order 81]] | |||
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| subgroup structure || [[subgroup structure of groups of order 81]] | |||
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| linear representation theory || [[linear representation theory of groups of order 81]] | |||
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==Statistics at a glance== | |||
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! Quantity !! Value | |||
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| Total number of groups || 15 | |||
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| Number of abelian groups || 5 | |||
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| Number of groups of class ''exactly'' two || 6 | |||
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| Number of groups of class ''exactly'' three || 4 | |||
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==The list== | ==The list== | ||
Revision as of 22:52, 28 March 2011
This article gives information about, and links to more details on, groups of order 81
See pages on algebraic structures of order 81 | See pages on groups of a particular order
This article gives basic information comparing and contrasting groups of order . See also more detailed information on specific subtopics through the links:
| Information type | Page summarizing information for groups of order 81 |
|---|---|
| element structure | element structure of groups of order 81 |
| subgroup structure | subgroup structure of groups of order 81 |
| linear representation theory | linear representation theory of groups of order 81 |
Statistics at a glance
| Quantity | Value |
|---|---|
| Total number of groups | 15 |
| Number of abelian groups | 5 |
| Number of groups of class exactly two | 6 |
| Number of groups of class exactly three | 4 |
The list
| Common name for group | Second part of GAP ID (GAP ID is (p^4, second part)) | Nilpotency class |
|---|---|---|
| Cyclic group:Z81 | 1 | 1 |
| Direct product of Z9 and Z9 | 2 | 1 |
| SmallGroup(81,3) | 3 | 2 |
| Nontrivial semidirect product of Z9 and Z9 | 4 | 2 |
| Direct product of Z27 and Z3 | 5 | 1 |
| Semidirect product of Z27 and Z3 | 6 | 2 |
| Wreath product of Z3 and Z3 | 7 | 3 |
| SmallGroup(81,8) | 8 | 3 |
| SmallGroup(81,9) | 9 | 3 |
| SmallGroup(81,10) | 10 | 3 |
| Direct product of Z9 and E9 | 11 | 1 |
| Direct product of prime-cube order group:U(3,3) and Z3 | 12 | 2 |
| Direct product of semidirect product of Z9 and Z3 and Z3 | 13 | 2 |
| Central product of prime-cube order group:U(3,3) and Z9 | 14 | 2 |
| Elementary abelian group:E81 | 15 | 1 |
Arithmetic functions
Functions taking values between 0 and 4
These measure ranks of subgroups, lengths of series, or the prime-base logarithms of orders of certain subgroups.