Groups of order 110: Difference between revisions
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| Number of [[abelian group]]s (i.e., [[finite abelian group]]s) up to isomorphism || [[abelian count::1]] || (number of abelian groups of order <math>2^1</math>) times (number of abelian groups of order <math>5^1</math>) times (number of abelian groups of order <math>11^1</math>) = ([[number of unordered integer partitions]] of 1) times ([[number of unordered integer partitions]] of 1) times ([[number of unordered integer partitions]] of 1) = <math>1 \times 1 \times 1 = 1</math>. {{abelian count explanation}} | | Number of [[abelian group]]s (i.e., [[finite abelian group]]s) up to isomorphism || [[abelian count::1]] || (number of abelian groups of order <math>2^1</math>) times (number of abelian groups of order <math>5^1</math>) times (number of abelian groups of order <math>11^1</math>) = ([[number of unordered integer partitions]] of 1) times ([[number of unordered integer partitions]] of 1) times ([[number of unordered integer partitions]] of 1) = <math>1 \times 1 \times 1 = 1</math>. {{abelian count explanation}} | ||
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==The list== | |||
{| class="sortable" border="1" | |||
! Group !! Second part of GAP ID (GAP ID is (20,second part)) !! abelian? | |||
|- | |||
| [[general affine group:GA(1,11)]] || 1 || No | |||
|- | |||
| [[direct product of Z2 and semidirect product of Z11 and Z5]] || 2 || No | |||
|- | |||
| [[direct product of Z11 and D10]] || 3 || No | |||
|- | |||
| [[direct product of Z5 and D22]] || 4 || No | |||
|- | |||
| [[dihedral group:D110]] || 5 || No | |||
|- | |||
| [[cyclic group:Z110]] || 6 || Yes | |||
|} | |} | ||
Revision as of 23:20, 17 November 2023
This article gives information about, and links to more details on, groups of order 110
See pages on algebraic structures of order 110 | See pages on groups of a particular order
Statistics at a glance
The number 110 has the prime factorization:
| Quantity | Value | Explanation |
|---|---|---|
| Total number of groups up to isomorphism | 6 | |
| Number of abelian groups (i.e., finite abelian groups) up to isomorphism | 1 | (number of abelian groups of order ) times (number of abelian groups of order ) times (number of abelian groups of order ) = (number of unordered integer partitions of 1) times (number of unordered integer partitions of 1) times (number of unordered integer partitions of 1) = . See classification of finite abelian groups and structure theorem for finitely generated abelian groups. |
The list
| Group | Second part of GAP ID (GAP ID is (20,second part)) | abelian? |
|---|---|---|
| general affine group:GA(1,11) | 1 | No |
| direct product of Z2 and semidirect product of Z11 and Z5 | 2 | No |
| direct product of Z11 and D10 | 3 | No |
| direct product of Z5 and D22 | 4 | No |
| dihedral group:D110 | 5 | No |
| cyclic group:Z110 | 6 | Yes |