Groups of order 42: Difference between revisions
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{{groups of order|42}} | {{groups of order|42}} | ||
==The list== | |||
There are, up to isomorphism, six groups of order 42, indicated in the table below: | There are, up to isomorphism, six groups of order 42, indicated in the table below: | ||
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| [[direct product of S3 and Z7]] || 3 || No | | [[direct product of S3 and Z7]] || 3 || No | ||
|- | |- | ||
| [[direct product of | | [[direct product of D14 and Z3]] || 4 || No | ||
|- | |- | ||
| [[dihedral group:D42]] || 5 || No | | [[dihedral group:D42]] || 5 || No | ||
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| [[cyclic group:Z42]] || 6 || Yes | | [[cyclic group:Z42]] || 6 || Yes | ||
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==Minimal order attaining number== | |||
<math>42</math> is the smallest number such that there are precisely <math>6</math> groups of that order up to isomorphism. That is, the value of the [[minimal order attaining function]] at <math>6</math> is <math>42</math>. | |||
==See also== | |||
[[Classification of groups of order two times a product of two distinct odd primes]] | |||
Latest revision as of 23:00, 9 December 2023
This article gives information about, and links to more details on, groups of order 42
See pages on algebraic structures of order 42 | See pages on groups of a particular order
The list
There are, up to isomorphism, six groups of order 42, indicated in the table below:
| Group | GAP ID (second part) | Abelian? |
|---|---|---|
| General affine group:GA(1,7), also known as F7 | 1 | No |
| direct product of Z2 and the semidirect product of Z7 and Z3 | 2 | No |
| direct product of S3 and Z7 | 3 | No |
| direct product of D14 and Z3 | 4 | No |
| dihedral group:D42 | 5 | No |
| cyclic group:Z42 | 6 | Yes |
Minimal order attaining number
is the smallest number such that there are precisely groups of that order up to isomorphism. That is, the value of the minimal order attaining function at is .
See also
Classification of groups of order two times a product of two distinct odd primes