A131932 Number of nonisomorphic nonsolvable groups of order A056866(n).

1, 3, 1, 1, 8, 1, 3, 6, 1, 26, 2, 2, 5, 2, 8, 23, 1, 6, 1, 107, 6, 1, 14, 1, 1, 1, 19, 2, 8, 28, 1, 93, 2, 4, 5, 5, 22, 1, 10, 1, 1, 588, 2, 20, 5, 1, 64, 4, 1, 5, 2, 5, 81, 1, 1, 18, 1, 25, 112, 2, 5, 1, 1

Offset: 1

Author

Artur Jasinski, Jul 30 2007, Oct 20 2007

Keywords

• nonn

Examples

			a(1) = 1 because there is only 1 nonsolvable group of order 60: A_5 (alternating group of 5th degree).
a(2) = 3 because there are 3 different nonsolvable groups of order 120.
		

Links

• O. L. Hoelder, Bildung zusammengesetzter Gruppen, Math. Ann., 46 (1895), 321-422; see p. 420.

Crossrefs

Cf. A001034, A060793, A056866, A056868.

Programs

GAP

NrUnsolvable := function(n) local i, count; count := 0; for i in [1..NumberSmallGroups(n)] do if not IsSolvableGroup(SmallGroup(n, i)) then count := count + 1; fi; od; return count; end; # Eric M. Schmidt, Apr 04 2013

GAP

LoadPackage("GrpConst"); NrUnsolvable := function(n) local i, j, num; num := 0; for i in DivisorsInt(n) do if i<>1 then for j in [1..NrPerfectGroups(i)] do num := num + Length(Remove(UpwardsExtensions(PerfectGroup(IsPermGroup, i, j), n/i))); od; fi; od; return num; end; # Eric M. Schmidt, Nov 14 2013

Extensions

Edited by N. J. A. Sloane, Oct 08 2007

More terms from Eric M. Schmidt, Apr 04 2013

a(44)-a(63) from Eric M. Schmidt, Nov 14 2013