Group cohomology of double cover of alternating group

This article gives specific information, namely, group cohomology, about a family of groups, namely: double cover of alternating group.
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Particular cases

$n$	$n!$ (order of the group $2\cdot A_{n}$)	The group $2\cdot A_{n}$	Is it a finite group with periodic cohomology?	Group cohomology information
4	24	special linear group:SL(2,3)	Yes	group cohomology of special linear group:SL(2,3)
5	120	special linear group:SL(2,5)	Yes	group cohomology of special linear group:SL(2,5)
6	720	special linear group:SL(2,9)	Yes	group cohomology of special linear group:SL(2,9)
7	5040	double cover of alternating group:A7	No	group cohomology of double cover of alternating group:A7
8	40320	double cover of alternating group:A8	No	group cohomology of double cover of alternating group:A8
9	362880	double cover of alternating group:A9	No	group cohomology of double cover of alternating group:A9