Groups of order 1536 - Revision history

Vipul at 15:46, 15 June 2011

2011-06-15T15:46:58Z

← Older revision		Revision as of 15:46, 15 June 2011
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	==GAP implementation==		==GAP implementation==

	~~The~~ order ~~1536 is part of~~ GAP~~'s [[GAP:SmallGroup~~\|~~SmallGroup]] library. Hence, all groups of~~ order 1536 ~~can be constructed using the [[GAP:SmallGroup~~\|~~SmallGroup]] function and have group IDs. However, [[GAP:IdGroup~~\|~~IdGroup]] is ''not'' available, i.e., given a group of order 1536, it is not possible to query the group ID directly.~~		{{this order in GAP\|order=1536\|idgroup = no\|listsizewarning = yes}}

	~~Here is GAP's summary information about how it stores groups of this order:~~

	<pre>gap> SmallGroupsInformation(1536);		<pre>gap> SmallGroupsInformation(1536);

Vipul at 21:08, 14 June 2011

2011-06-14T21:08:16Z

← Older revision		Revision as of 21:08, 14 June 2011
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	{{groups of order\|1536}}		{{groups of order\|1536}}

			==Statistics at a glance==

			The number 1536 has prime factorization <math>1536 = 3 \cdot 2^9</math>. Because the order has only two distinct prime factors, and [[order has only two prime factors implies solvable]], all groups of this order are [[solvable group]]s.

			{\| class="sortable" border="1"
			! Quantity !! Value !! Explanation
			\|-
			\| Number of groups up to isomorphism \|\| 408641062 \|\|
			\|-
			\| Number of [[abelian group]] up to isomorphism \|\| 30 \|\| (number of abelian groups of order <math>2^9</math>) times (number of abelian groups of order <math>3^1</math>) = ([[number of unordered integer partitions]] of <math>9</math>) times ([[number of unordered integer partitions]] of <math>1</math>) = <math>30 \times 1 = 30</math>
			\|-
			\| Number of [[nilpotent group]]s up to isomorphism \|\| 10494213 \|\| (number of [[groups of order 512]]) times (number of [[groups of order 3]]) = <math>10494213 \times 1 = 10494213</math>
			\|-
			\| Number of [[solvable group]]s up to isomorphism \|\| 408641062 \|\| Because the order has only two distinct prime factors, and [[order has only two prime factors implies solvable]], all groups of this order are [[solvable group]]s.
			\|}
	==GAP implementation==		==GAP implementation==

Vipul: Created page with "{{groups of order|1536}} ==GAP implementation== The order 1536 is part of GAP's SmallGroup library. Hence, all groups of order 1536 can be constructed using ..."

2011-06-14T21:04:04Z

Created page with "{{groups of order|1536}} ==GAP implementation== The order 1536 is part of GAP's SmallGroup library. Hence, all groups of order 1536 can be constructed using ..."

New page

{{groups of order|1536}}

==GAP implementation==

The order 1536 is part of GAP's [[GAP:SmallGroup|SmallGroup]] library. Hence, all groups of order 1536 can be constructed using the [[GAP:SmallGroup|SmallGroup]] function and have group IDs. However, [[GAP:IdGroup|IdGroup]] is ''not'' available, i.e., given a group of order 1536, it is not possible to query the group ID directly.

Here is GAP's summary information about how it stores groups of this order:

<pre>gap> SmallGroupsInformation(1536);

There are 408641062 groups of order 1536.
1 - 10494213 are the nilpotent groups.
10494214 - 408526597 have a normal Sylow 3-subgroup.
408526598 - 408544625 have a normal Sylow 2-subgroup.
408544626 - 408641062 have no normal Sylow subgroup.

This size belongs to layer 8 of the SmallGroups library.
IdSmallGroup is not available for this size.</pre>