Difference between revisions of "Groups of order 48"

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(Sylow subgroups)
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! Quantity !! Value
 
! Quantity !! Value
 
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| Total number of groups || 52
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| Total number of groups || [[count::52]]
 
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| Number of abelian groups || 5
 
| Number of abelian groups || 5

Revision as of 16:35, 15 June 2011

This article gives information about, and links to more details on, groups of order 48
See pages on algebraic structures of order 48| See pages on groups of a particular order

This article gives basic information comparing and contrasting groups of order 48.

Statistics at a glance

Quantity Value
Total number of groups 52
Number of abelian groups 5
Number of nilpotent groups 14
Number of solvable groups 52
Number of simple groups 0

Sylow subgroups

2-Sylow subgroups

Here is the occurrence summary:

Group of order 16 GAP ID (second part) Number of groups of order 48 in which it is a 2-Sylow subgroup List of these groups Second part of GAP ID of these groups
cyclic group:Z16 1 2 1, 2
direct product of Z4 and Z4 2 3 3, 11, 20
SmallGroup(16,3) 3 4 14, 19, 21, 30
nontrivial semidirect product of Z4 and Z4 4 3 12, 13, 22
direct product of Z8 and Z2 5 3 4, 9, 23
M16 6 3 5, 10, 24
dihedral group:D16 7 3 7, 15, 25
semidihedral group:SD16 8 5 6, 16, 17, 26, 29
generalized quaternion group:Q16 9 4 8, 18, 27, 28
direct product of Z4 and V4 10 4 31, 35, 42, 44
direct product of D8 and Z2 11 5 36, 38, 43, 45, 48
direct product of Q8 and Z2 12 4 32, 34, 40, 46
central product of D8 and Z4 13 5 33, 37, 39, 41, 47
elementary abelian group:E16 14 4 49, 50, 51, 52