R-a-jones at 23:18, 9 December 2023

2023-12-09T23:18:12Z

← Older revision		Revision as of 23:18, 9 December 2023
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	All groups of this order are [[solvable group]]s, and in particular, [[finite solvable group]]s, so 140 is a [[solvability-forcing number]].		All groups of this order are [[solvable group]]s, and in particular, [[finite solvable group]]s, so 140 is a [[solvability-forcing number]].

			==Minimal order attaining number==

			<math>140</math> is the smallest number such that there are precisely <math>11</math> groups of that order up to isomorphism. That is, the value of the [[minimal order attaining function]] at <math>11</math> is <math>140</math>.

	==GAP implementation==		==GAP implementation==

Vipul: Created page with "{{groups of order|140}} ==Statistics at a glance== The number 140 has prime factors 2, 5, and 7. The prime factorization is: $\! 140 = 2^2 \cdot 5^1 \cdot 7^1 = 4 \cdot 5..."$

2011-08-17T02:02:59Z

Created page with "{{groups of order|140}} ==Statistics at a glance== The number 140 has prime factors 2, 5, and 7. The prime factorization is: <math>\! 140 = 2^2 \cdot 5^1 \cdot 7^1 = 4 \cdot 5..."

New page

{{groups of order|140}}

==Statistics at a glance==

The number 140 has prime factors 2, 5, and 7. The prime factorization is:

<math>\! 140 = 2^2 \cdot 5^1 \cdot 7^1 = 4 \cdot 5 \cdot 7</math>

All groups of this order are [[solvable group]]s, and in particular, [[finite solvable group]]s, so 140 is a [[solvability-forcing number]].

==GAP implementation==

{{this order in GAP|order = 140|idgroup = yes}}

<pre>gap> SmallGroupsInformation(140);

There are 11 groups of order 140.
They are sorted by their Frattini factors.
1 has Frattini factor [ 70, 1 ].
2 has Frattini factor [ 70, 2 ].
3 has Frattini factor [ 70, 3 ].
4 has Frattini factor [ 70, 4 ].
5 - 11 have trivial Frattini subgroup.

For the selection functions the values of the following attributes
are precomputed and stored:
IsAbelian, IsNilpotentGroup, IsSupersolvableGroup, IsSolvableGroup,
LGLength, FrattinifactorSize and FrattinifactorId.

This size belongs to layer 2 of the SmallGroups library.
IdSmallGroup is available for this size.</pre>

Groups of order 140 - Revision history

R-a-jones at 23:18, 9 December 2023

Vipul: Created page with "{{groups of order|140}} ==Statistics at a glance== The number 140 has prime factors 2, 5, and 7. The prime factorization is: \! 140 = 2^2 \cdot 5^1 \cdot 7^1 = 4 \cdot 5..."

Vipul: Created page with "{{groups of order|140}} ==Statistics at a glance== The number 140 has prime factors 2, 5, and 7. The prime factorization is: $\! 140 = 2^2 \cdot 5^1 \cdot 7^1 = 4 \cdot 5..."$