Difference between revisions of "Symmetric group:S7"

From Groupprops
Jump to: navigation, search
(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)
Line 16: Line 16:
 
| {{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>
 
| {{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>
 
|-
 
|-
| {{arithmetic function value|Frattini length|1}}
+
| {{arithmetic function value given order|Frattini length|1}}
 
|}
 
|}

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 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 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