A124901 Smallest order of any nonsolvable transitive Galois group for a polynomial of degree n.

60, 60, 168, 168, 504, 60, 660, 60, 5616, 168, 60, 336, 4080, 180, 60822550204416000, 60, 168, 1320, 10200960, 120, 300, 5616, 1512, 168, 4420880996869850977271808000000, 60

Offset: 5

Author

Artur Jasinski, Nov 12 2006

Keywords

• nonn

Comments

These transitive groups are in MAGMA classification respectively:

a(5)=5T4, a(6)=6T12, a(7)=7T5, a(8)=8T37, a(9)=9T27,

a(10)=10T6, a(11)=11T5, a(12)=12T33, a(13)=13T7, a(14)=14T10,

a(15)=15T5, a(16)=16T713, a(17)=17T6, a(18)=18T90, a(19)=19T7,

a(20)=20T15, a(21)=21T14, a(22)=22T13, a(23)=23T4,

a(24)=24T201, a(25)=25T29, a(26)=26T39, a(27)=27T390,

a(28)=28T32, a(29)=28T7, a(30)=30T9.

Examples

			a(8)=336 because nonsolvable Galois group PGL(2,7)=L(8) has order 336.
		

Crossrefs

Cf. A124900, A186772.

Extensions

a(4) corrected and a(11)-a(30) by Artur Jasinski, Feb 26 2011