Groups of order 24: Difference between revisions
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| [[direct product of E8 and Z3]] || 15 | | [[direct product of E8 and Z3]] || 15 | ||
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==Sylow subgroups== | |||
===2-Sylow subgroups | |||
{| class="sortable" border="1" | |||
! Group !! Second part of GAP ID (ID is (24,second part)) !! 2-Sylow subgroup !! Second part of GAP ID !! Number of 2-Sylow subgroups | |||
|- | |||
| [[nontrivial semidirect product of Z3 and Z8]] || 1 || [[cyclic group:Z8]] || 1 || 3 | |||
|- | |||
| [[cyclic group:Z24]] || 2 || [[cyclic group:Z8]] || 1 || 1 | |||
|- | |||
| [[special linear group:SL(2,3)]] || 3 || [[quaternion group]] || 4 || 1 | |||
|- | |||
| [[dicyclic group:Dic24]] || 4 || [[quaternion group]] || 4 || 3 | |||
|- | |||
| [[direct product of S3 and Z4]] || 5 || [[direct product of Z4 and Z2]] || 2 || 3 | |||
|- | |||
| [[dihedral group:D24]] || 6 || [[dihedral group:D8]] || 3 || 3 | |||
|- | |||
| [[direct product of Dic12 and Z2]] || 7 || [[direct product of Z4 and Z2]] || 2 || 3 | |||
|- | |||
| [[SmallGroup(24,8)]] || 8 || [[dihedral group:D8]] || 3 || 3 | |||
|- | |||
| [[direct product of Z6 and Z4]] (also, direct product of Z12 and Z2) || 9 || [[direct product of Z4 and Z2]] || 2 || 1 | |||
|- | |||
| [[direct product of D8 and Z3]] || 10 || [[dihedral group:D8]] || 3 || 1 | |||
|- | |||
| [[direct product of Q8 and Z3]] || 11 || [[quaternion group]] || 4 || 1 | |||
|- | |||
| [[symmetric group:S4]] || 12 || [[dihedral group:D8]] || 3 || 3 | |||
|- | |||
| [[direct product of A4 and Z2]] || 13 || [[elementary abelian group:E8]] || 5 || 1 | |||
|- | |||
| [[direct product of D12 and Z2]] (also direct product of S3 and V4) || 14 || [[elementary abelian group:E8]] || 5 || 3 | |||
|- | |||
| [[direct product of E8 and Z3]] || 15 || [[elementary abelian group:E8]] || 5 || 1 | |||
|} | |} | ||
Revision as of 02:58, 30 October 2010
The list
There are 15 groups of order 24.
| Group | Second part of GAP ID (ID is (24,second part)) |
|---|---|
| nontrivial semidirect product of Z3 and Z8 | 1 |
| cyclic group:Z24 | 2 |
| special linear group:SL(2,3) | 3 |
| dicyclic group:Dic24 | 4 |
| direct product of S3 and Z4 | 5 |
| dihedral group:D24 | 6 |
| direct product of Dic12 and Z2 | 7 |
| SmallGroup(24,8) | 8 |
| direct product of Z6 and Z4 (also, direct product of Z12 and Z2) | 9 |
| direct product of D8 and Z3 | 10 |
| direct product of Q8 and Z3 | 11 |
| symmetric group:S4 | 12 |
| direct product of A4 and Z2 | 13 |
| direct product of D12 and Z2 (also direct product of S3 and V4) | 14 |
| direct product of E8 and Z3 | 15 |
Sylow subgroups
===2-Sylow subgroups