Alternating group:A10

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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