Difference between revisions of "Symmetric group:S7"

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(Arithmetic functions)
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! Function !! Value !! Explanation
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! Function !! Value !! Similar groups !! Explanation
 
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| {{arithmetic function value order|5040}} The order is <math>7! = 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1</math>
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| {{arithmetic function value order|5040}}|| The order is <math>7! = 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1</math>
 
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| {{arithmetic function value given order|exponent of a group|420}} The exponent is the least common multiple of <math>1,2,3,4,5,6,7</math>
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| {{arithmetic function value given order|exponent of a group|420}}|| The exponent is the least common multiple of <math>1,2,3,4,5,6,7</math>
 
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| {{arithmetic function value given order|Frattini length|1}}
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| {{arithmetic function value given order|Frattini length|1}}||
 
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Revision as of 01:41, 2 November 2010

This article is about a particular group, i.e., a group unique upto isomorphism. View specific information (such as linear representation theory, subgroup structure) about this group
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Definition

This group is a finite group defined as the symmetric group on a set of size 7. The set is typically taken to be \{ 1,2,3,4,5,6,7 \}.

In particular, it is a symmetric group on finite set as well as a symmetric group of prime degree.

Arithmetic functions

Function Value Similar groups Explanation
order (number of elements, equivalently, cardinality or size of underlying set) 5040 groups with same order The order is 7! = 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1
exponent of a group 420 groups with same order and exponent of a group
"{{{" can not be assigned to a declared number type with value 3.
| groups with same exponent of a group
The exponent is the least common multiple of 1,2,3,4,5,6,7
Frattini length 1 groups with same order and Frattini length
"{{{" can not be assigned to a declared number type with value 3.
| groups with same Frattini length