Generators and Representations for G = HN

Standard generators

• Standard generators of the Harada-Norton group HN are a and b where a is in class 2A, b is in class 3B, ab has order 22 and ababb has order 5. (Source: ATLAS)
• Standard generators of its automorphism group HN:2 are c and d where c is in class 2C, d is in class 5A and cd has order 42. (Source: ATLAS)

BBOX programs

• Finder for HN
• Finder for HN.2
• Checker for HN
• Checker for HN.2
• CCL rep tester for HN

Representations

Representation genus			Representations available			Test results		Miscellaneous information
Group	Dim	Ind	File	Char	Ring	Checker	CCL	Sparsity	Max	Size (Kb)	Comments
HN	133	+	133(a)	χ2	C			51%		251.8	John Bray: http://web.mat.bham.ac.uk/spres/Spor/HN/
			133(b)	χ3	C			51%		251.7	John Bray: http://web.mat.bham.ac.uk/spres/Spor/HN/

Notes

Element abababb is in class 20D.

Last generated on Sat Sep 24 18:52:42 2005