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A060653
Minimal number of conjugacy classes (which is also the number of irreducible representations) in G where G is a finite group of order n.
2
1, 2, 3, 4, 5, 3, 7, 5, 9, 4, 11, 4, 13, 5, 15, 7, 17, 6, 19, 5, 5, 7, 23, 5, 25, 8, 11, 10, 29, 9, 31, 11, 33, 10, 35, 6, 37, 11, 7, 10, 41, 7, 43, 14, 45, 13, 47, 8, 49, 14, 51, 7, 53, 10, 7, 8, 9, 16, 59, 5, 61, 17, 15, 13, 65, 18, 67, 8, 69, 19, 71, 6, 73
OFFSET
1,2
COMMENTS
a(n) <= n with equality iff n belongs to sequence A051532.
LINKS
EXAMPLE
a(6) = 3 because there are two groups of order 6, the cyclic group with 6 classes and S_3 with 3 classes.
PROG
(GAP) A060653 := function(n) local min, i; min := n; for i in [1..NumberSmallGroups(n)] do min := Minimum(min, NrConjugacyClasses(SmallGroup(n, i))); od; return min; end; # Eric M. Schmidt, Aug 30 2012
CROSSREFS
KEYWORD
nonn
AUTHOR
Noam Katz (noamkj(AT)hotmail.com), Apr 17 2001
EXTENSIONS
More terms from Eric M. Schmidt, Aug 30 2012
STATUS
approved