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Symmetric group:S7

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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 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