Difference between revisions of "Symmetric group:S7"
From Groupprops
(Created page with "{{particular group}} ==Definition== This group is a finite group defined as the member of family::symmetric group on a set of size <math>7</math>. The set is typica...") 
(→Arithmetic functions) 

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 {{arithmetic function value given orderexponent of a group420}} The exponent is the least common multiple of <math>1,2,3,4,5,6,7</math>   {{arithmetic function value given orderexponent of a group420}} The exponent is the least common multiple of <math>1,2,3,4,5,6,7</math>  
    
−   {{arithmetic function valueFrattini length1}}  +   {{arithmetic function value given orderFrattini length1}} 
}  } 
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
View a complete list of particular groups (this is a very huge list!)[SHOW MORE]
Definition
This group is a finite group defined as the symmetric group on a set of size . The set is typically taken to be .
In particular, it is a symmetric group on finite set as well as a symmetric group of prime degree.
Arithmetic functions
Function  Value  Explanation 

order (number of elements, equivalently, cardinality or size of underlying set)  5040  groups with same order The order is 
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

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
