Symmetric group:S8

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VIEW FACTS ABOUT THIS GROUP: All factsGroup property satisfactionsSubgroup property satisfactionsGroup property dissatisfactionsSubgroup property satisfactions
VIEW DEFINITIONS USING THIS AS EXAMPLE: All terms |Group properties |Subgroup properties|
VIEW FACTS USING THIS AS EXAMPLE: All facts |Group property non-implications |Subgroup property non-implications |Group metaproperty dissatisfactionsSubgroup metaproperty dissatisfactions

Definition

This group is a finite group defined as the symmetric group on a set of size $8$. The set is typically taken to be $\{1,2,3,4,5,6,7,8\}$.

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

Arithmetic functions

Function	Value	Similar groups	Explanation
order (number of elements, equivalently, cardinality or size of underlying set)	40320	groups with same order	The order is $8!=8\cdot 7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1$
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 $1,2,3,4,5,6,7,8$
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