

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
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OFFSET

1,2


COMMENTS

a(n) <= n with equality iff n belongs to sequence A051532.


LINKS

Eric M. Schmidt, Table of n, a(n) for n = 1..1023


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

A051532.
Sequence in context: A275823 A141295 A134198 * A274690 A081810 A071829
Adjacent sequences: A060650 A060651 A060652 * A060654 A060655 A060656


KEYWORD

nonn


AUTHOR

Noam Katz (noamkj(AT)hotmail.com), Apr 17 2001


EXTENSIONS

More terms from Eric M. Schmidt, Aug 30 2012


STATUS

approved



