Groups of order 21: Difference between revisions
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| [[cyclic group:Z21]] || 2 || Yes | | [[cyclic group:Z21]] || 2 || Yes | ||
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This is classified by the [[classification of groups of order a product of two distinct primes]] in the case with two isomorphism classes since <math>21 = 3 \cdot 7</math>, with <math>3 \mid 7-1</math>. | |||
Z7⋊Z3 is the smallest non-abelian group of odd order. | Z7⋊Z3 is the smallest non-abelian group of odd order. | ||
Revision as of 00:42, 3 November 2023
This article gives information about, and links to more details on, groups of order 21
See pages on algebraic structures of order 21 | See pages on groups of a particular order
There are, up to isomorphism, two groups of order 21, indicated in the table below:
| Group | GAP ID (second part) | Abelian? |
|---|---|---|
| Frobenius group: Z7⋊Z3 | 1 | No |
| cyclic group:Z21 | 2 | Yes |
This is classified by the classification of groups of order a product of two distinct primes in the case with two isomorphism classes since , with .
Z7⋊Z3 is the smallest non-abelian group of odd order.