Double cover of symmetric group:S5 of plus type
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This group is defined as the double cover of symmetric group of "+" type for symmetric group:S5, and is denoted . In particular, it is one of the two stem extensions where the base normal subgroup is cyclic group:Z2 and the quotient group is symmetric group:S5.
Want to compare and contrast arithmetic function values with other groups of the same order? Check out groups of order 240#Arithmetic functions
|order (number of elements, equivalently, cardinality or size of underlying set)||240||groups with same order||order of extension group is product of order of normal subgroup and quotient group: The order is|
This finite group has order 240 and has ID 90 among the groups of order 240 in GAP's SmallGroup library. For context, there are 208 groups of order 240. It can thus be defined using GAP's SmallGroup function as:
For instance, we can use the following assignment in GAP to create the group and name it :
gap> G := SmallGroup(240,90);
Conversely, to check whether a given group is in fact the group we want, we can use GAP's IdGroup function:
IdGroup(G) = [240,90]
or just do:
to have GAP output the group ID, that we can then compare to what we want.