Generators and Representations for G = F₂₂

Standard generators

• Standard generators of the Fischer group Fi₂₂ are a and b where a is in class 2A, b has order 13, ab has order 11 and ababababbababbabb has order 12. (Source: ATLAS)
• Standard generators of the double cover 2.Fi₂₂ are preimages A and B where B has order 13 and AB has order 11. (Source: ATLAS)
• Standard generators of the triple cover 3.Fi₂₂ are preimages A and B where A has order 2 and B has order 13. The canonical central element is (AB)²² (Source: ATLAS)
• Standard generators of the automorphism group Fi₂₂:2 are c and d where c is in class 2A, d is in class 18E and cd has order 42. (Source: ATLAS)

BBOX programs

• Finder for F₂₂
• Finder for F₂₂.2
• Checker for F₂₂
• Checker for F₂₂.2
• CCL rep tester for F₂₂

Representations

Representation genus			Representations available			Test results		Miscellaneous information
Group	Dim	Ind	File	Char	Ring	Checker	CCL	Sparsity	Max	Size (Kb)	Comments
F22	78	+	78	χ2	Z			70%	60	27.8	ATLAS, reseeded by some null vector (can't remember), LLL'ed

Last generated on Sat Sep 24 18:52:44 2005