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A131932
Number of nonisomorphic nonsolvable groups of order A056866(n).
4
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
1,2
LINKS
O. L. Hoelder, Bildung zusammengesetzter Gruppen, Math. Ann., 46 (1895), 321-422; see p. 420.
EXAMPLE
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.
PROG
(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
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
Artur Jasinski, Jul 30 2007, Oct 20 2007
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
STATUS
approved