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%I #13 Mar 12 2020 07:07:32
%S 60,60,168,168,504,60,660,60,5616,168,60,336,4080,180,
%T 60822550204416000,60,168,1320,10200960,120,300,5616,1512,168,
%U 4420880996869850977271808000000,60
%N Smallest order of any nonsolvable transitive Galois group for a polynomial of degree n.
%C These transitive groups are in MAGMA classification respectively:
%C a(5)=5T4, a(6)=6T12, a(7)=7T5, a(8)=8T37, a(9)=9T27,
%C a(10)=10T6, a(11)=11T5, a(12)=12T33, a(13)=13T7, a(14)=14T10,
%C a(15)=15T5, a(16)=16T713, a(17)=17T6, a(18)=18T90, a(19)=19T7,
%C a(20)=20T15, a(21)=21T14, a(22)=22T13, a(23)=23T4,
%C a(24)=24T201, a(25)=25T29, a(26)=26T39, a(27)=27T390,
%C a(28)=28T32, a(29)=28T7, a(30)=30T9.
%e a(8)=336 because nonsolvable Galois group PGL(2,7)=L(8) has order 336.
%Y Cf. A124900, A186772.
%K nonn
%O 5,1
%A _Artur Jasinski_, Nov 12 2006
%E a(4) corrected and a(11)-a(30) by _Artur Jasinski_, Feb 26 2011
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