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A131932 Number of nonisomorphic nonsolvable groups of order A056866(n). 4

%I #21 Mar 13 2015 22:43:24

%S 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,

%T 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,

%U 2,5,1,1

%N Number of nonisomorphic nonsolvable groups of order A056866(n).

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

%e a(1) = 1 because there is only 1 nonisomorphic and nonsolvable group of order 60: A_5 (alternating group of 5th degree).

%e a(2) = 3 because there are 3 different nonisomorphic and nonsolvable groups of order 120.

%o (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

%o (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

%Y Cf. A001034, A060793, A056866, A056868.

%K nonn

%O 1,2

%A _Artur Jasinski_, Jul 30 2007, Oct 20 2007

%E Edited by _N. J. A. Sloane_, Oct 08 2007

%E More terms from _Eric M. Schmidt_, Apr 04 2013

%E a(44)-a(63) from _Eric M. Schmidt_, Nov 14 2013

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Last modified March 28 16:28 EDT 2024. Contains 371254 sequences. (Running on oeis4.)