Endomorphism structure of groups of order 36: Difference between revisions
| Line 26: | Line 26: | ||
| [[SmallGroup(36,9)]] || 9 || [[General semiaffine group:GammaA(1,9)]] || 144 | | [[SmallGroup(36,9)]] || 9 || [[General semiaffine group:GammaA(1,9)]] || 144 | ||
|- | |- | ||
| [[Direct product of S3 and S3]] || 10 || || 72 | | [[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 | | [[Direct product of A4 and Z3]] || 11 || [[Direct product of S3 and S4]] || 144 | ||
Revision as of 03:39, 29 December 2023
This page discusses the endomorphism structure of groups of order 36.
Automorphism group
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 | SmallGroup(108,26) | 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 | SmallGroup(108,26) | 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 | 864 | |
| Direct product of E4 and E9 | 14 | 288 |