A198342 Number of non-solvable transitive permutation groups for polynomials of degree n.

0, 0, 0, 0, 2, 4, 3, 5, 4, 21, 4, 36, 3, 27, 40, 49, 5, 91, 2, 358, 56, 27, 3, 807, 79, 26, 64, 617, 2, 1896, 4

Offset: 1

Author

Artur Jasinski, Oct 23 2011

Keywords

• nonn
• hard
• more

Comments

For prime degrees of polynomials see A201443.

All non-solvable groups are non-commutative.

Is this the same as A124938 ? - R. J. Mathar, Oct 04 2018

Examples

			a(4)=0 because for quartic polynomials all groups are solvable.
a(5)=2 because for quintic polynomials we have two non-solvable groups: A(5) and S(5).
		

Links

• A. Bialostocki and T. Shaska, Galois groups of prime degree polynomials with nonreal roots, 2006.

Crossrefs

Cf. A002106, A131932.

Programs

Magma

// for a(16):
for g in [1..1954] do
G:=TransitiveGroup(16,g);
IsSolvable(G);
end for