Endomorphism structure of groups of order 36: Difference between revisions
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{{all given order groups-specific information| | |||
information type = endomorphism structure| | |||
order = 36| | |||
connective = of}} | |||
This page discusses the endomorphism structure of [[groups of order 36]]. | This page discusses the endomorphism structure of [[groups of order 36]]. | ||
==Automorphism | ==Automorphism groups== | ||
The automorphism groups of the groups are as follows: | The automorphism groups of the groups are as follows: | ||
{ | {{Groups of order 36 automorphism groups}} | ||
Latest revision as of 03:58, 29 December 2023
This article gives specific information, namely, endomorphism structure, about a family of groups, namely: groups of order 36.
View endomorphism structure of group families | View endomorphism structure of groups of a particular order |View other specific information about groups of order 36
This page discusses the endomorphism structure of groups of order 36.
Automorphism groups
The automorphism groups of the groups are as follows:
| Group | Second part of GAP ID | Isomorphism class of automorphism group | Automorphism group order |
|---|---|---|---|
| Dicyclic group:Dic36 | 1 | Direct product of Z2 and SmallGroup(54,6) | 108 |
| Cyclic group:Z36 | 2 | Direct product of Z6 and Z2 | 12 |
| SmallGroup(36,3) | 3 | Direct product of S4 and Z3 | 72 |
| Dihedral group:D36 | 4 | Direct product of Z2 and SmallGroup(54,6) | 108 |
| Direct product of E4 and Z9 | 5 | Direct product of D12 and Z3 | 36 |
| SmallGroup(36,6) | 6 | Direct product of D12 and Z2 | 24 |
| SmallGroup(36,7) | 7 | Direct product of Z2 and GA(2,3) | 864 |
| Direct product of E9 and Z4 | 8 | Direct product of Z2 and GL(2,3) | 96 |
| SmallGroup(36,9) | 9 | General semiaffine group:GammaA(1,9) | 144 |
| Direct product of S3 and S3 | 10 | Wreath product of S3 and Z2 | 72 |
| Direct product of A4 and Z3 | 11 | Direct product of S3 and S4 | 144 |
| SmallGroup(36,12) | 12 | Direct product of D12 and Z2 | 24 |
| SmallGroup(36,13) | 13 | Direct product of Z2 and GA(2,3) | 864 |
| Direct product of E4 and E9 | 14 | Direct product of S3 and GL(2,3) | 288 |