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.

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

Author

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

Keywords

• nonn

Comments

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

Examples

			a(6) = 3 because there are two groups of order 6, the cyclic group with 6 classes and S_3 with 3 classes.
		

Links

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

Crossrefs

A051532.

Programs

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

Extensions

More terms from Eric M. Schmidt, Aug 30 2012