Generators and Representations for G = A₁₀

Standard generators

• Standard generators of A₁₀ are a and b where a is in class 3A, b has order 9, ab has order 8 and abb has order 12. (Source: ATLAS)
• Standard generators of the double cover 2.A₁₀ are preimages A and B where A has order 3 and B has order 9. (Source: ATLAS)

BBOX programs

• Finder for A₁₀
• Checker for A₁₀
• CCL rep tester for A₁₀

Representations

Representation genus			Representations available			Test results		Miscellaneous information
Group	Dim	Ind	File	Char	Ring	Checker	CCL	Sparsity	Max	Size (Kb)	Comments
A10	9	+	9	χ2	Z			83%	1	0.8	Young rep 91
A10	35	+	35	χ3	Z			92%	1	5.7	Young rep 82
A10	36	+	36	χ4	Z			95%	1	5.9	Young rep 811
A10	42	+	42	χ5	Z			87%	2	8.0	Young rep 55
A10	75	+	75	χ6	Z			94%	1	24.0	Young rep 73
A10	84	+	84	χ7	Z			97%	1	29.6	Young rep 7111
A10	90	+	90	χ8	Z			94%	2	34.1	Young rep 64
A10	126	+	126	χ9	Z			98%	1	65.6	Young rep 61111
A10	160	+	160	χ10	Z			97%	1	105.8	Young rep 721
A10	210	+	210	χ11	Z			94%	3	183.4	Young rep 433
A10	224	+	224(a)	χ12	Z			68%	109	231.6	perm rep on 1200 pts, LLL'ed
			224(b)	χ13	Z			55%	136	241.9	automorph of χ12
A10	225	+	225	χ14	Z			97%	2	209.7	Young rep 622
2.A10	16	+	No representations available
2.A10	48	o	No representations available
2.A10	64	+	No representations available
2.A10	216	+	No representations available

Notes

Element y is in class 9A.

Last generated on Sat Sep 24 18:52:48 2005