Alternating group:A10

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VIEW DEFINITIONS USING THIS AS EXAMPLE: All terms |Group properties |Subgroup properties|
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Definition

This group is defined as the alternating group of degree 10, i.e., the alternating group on a set of size 10. This can be taken as the group on $\{1,2,3,4,5,6,7,8,9,10\}$.

Arithmetic functions

Function	Value	Similar groups	Explanation
order (number of elements, equivalently, cardinality or size of underlying set)	1814400	groups with same order	As $A_{n},n=10$: $n!/2=10!/2=(10\cdot 9\cdot 8\cdot 7\cdot 6\cdot \dots \cdot 2\cdot 1)/2=1814400$
exponent of a group	2520	groups with same order and exponent of a group | groups with same exponent of a group

GAP implementation

Description	Functions used	Explanation
AlternatingGroup(10)	AlternatingGroup