A061064 Maximal number of zeros in the character table of a group with n elements.

0, 0, 0, 0, 0, 1, 0, 3, 0, 2, 0, 4, 0, 3, 0, 12, 0, 9, 0, 8, 4, 5, 0, 27, 0, 6, 16, 12, 0, 25, 0, 48, 0, 8, 0, 36, 0, 9, 8, 75, 0, 49, 0, 20, 0, 11, 0, 108, 0, 50, 0, 24, 0, 81, 8, 147, 12, 14, 0, 100, 0, 15, 36, 192, 0, 121, 0, 32, 0, 98, 0, 243, 0, 18, 16

Offset: 1

Author

Ahmed Fares (ahmedfares(AT)my-deja.com), Jun 05 2001

Keywords

• nonn
• nice

Comments

A finite non-Abelian group G has an irreducible representation of degree >= 2 and the character of such representation always has a zero; so a(n) = 0 iff every group of order n is Abelian, i.e. n belongs to A051532.

Examples

			a(6) = 1 because the character table of the symmetric group S_3 is / 1, 1, 1 / 1, 1, -1 / 2, -1, 0 /.
		

Links

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

Crossrefs

Cf. A051532.

Programs

GAP

A061064 := function(n) local max, i; max := 0; for i in [1..NumberSmallGroups(n)] do max := Maximum(max, Sum(Irr(SmallGroup(n,i)), chi->Number(chi, x->x=0))); od; return max; end; # Eric M. Schmidt, Aug 24 2012

Extensions

Added terms a(n) for n>=24, Eric M. Schmidt, Aug 24 2012.