Generators and Representations for G = A₅

Standard generators

• Standard generators of A₅ are a and b where a has order 2, b has order 3 and ab has order 5. (Source: ATLAS)
• Standard generators of the double cover 2.A₅ (or SL₂(5)) are preimages A and B where B has order 3 and AB has order 5. (Source: ATLAS)

BBOX programs

• Checker for A₅
• CCL rep tester for A₅

Representations

Representation genus			Representations available			Test results		Miscellaneous information
Group	Dim	Ind	File	Char	Ring	Checker	CCL	Sparsity	Max	Size (Kb)	Comments
A5	3	+	3(a)	χ2	C			55%		0.5	Galois conjugate of χ3
			3(b)	χ3	C			55%		0.6	split up Young rep of S5 by taking 2dim +1 espace of AB and eliminating the unknown to find a splitting vector [l,1,l,-1,1,l], where l = 2 +/- Sqrt(5)
A5	4	+	4	χ4	Z			56%	1	0.5	young rep
A5	5	+	5	χ5	Z			60%	1	0.5	young rep
2.A5	2	-	2(a)	χ6	C			37%		0.5	worked it out on paper
2.A5	4	-	No representations available
2.A5	6	-	No representations available

Last generated on Sat Sep 24 18:52:45 2005