Generators and Representations for G = A₉

Standard generators

• Standard generators of A₉ are a and b where a is in class 3A, b has order 7 and ab has order 9. (Source: ATLAS)
• Standard generators of the double cover 2.A₉ are preimages A and B where A has order 3, and B has order 7. (Source: ATLAS)

BBOX programs

• Finder for A₉
• Checker for A₉
• CCL rep tester for A₉

Representations

Representation genus			Representations available			Test results		Miscellaneous information
Group	Dim	Ind	File	Char	Ring	Checker	CCL	Sparsity	Max	Size (Kb)	Comments
A9	8	+	8	χ2	Z			82%	1	0.7	Young rep 81
A9	21	o	21(a)	χ3	C			9%		71.4	complex conjugate of χ4
			21(b)	χ4	C			9%		71.4	rho-split Young rep
A9	27	+	27	χ5	Z			92%	1	3.5	Young rep 72
A9	28	+	28	χ6	Z			93%	1	3.7	Young rep 711
A9	35	+	35(a)	χ7	Z			79%	4	5.8	perm rep on 120a pts
			35(b)	χ8	Z			79%	3	5.8	perm rep on 120b pts
A9	42	+	42	χ9	Z			90%	2	8.0	Young rep 54
A9	48	+	48	χ10	Z			92%	1	10.1	Young rep 63
A9	56	+	56	χ11	Z			96%	1	13.4	Young rep 6111
A9	84	+	84	χ12	Z			94%	1	29.8	Young rep 441
A9	105	+	105	χ13	Z			96%	1	46.2	Young rep 621
A9	120	+	120	χ14	Z			96%	2	59.9	Young rep 522
A9	162	+	162	χ15	Z			96%	1	109.5	Young rep 531
A9	168	+	168	χ16	Z			95%	2	117.7	Young rep 432
A9	189	+	189	χ17	Z			97%	1	147.3	Young rep 5211
A9	216	+	216	χ18	Z			97%	1	192.7	Young rep 4311
2.A9	8	+	8(a)	χ19	C			73%		1.0	nicer(ish) basis
2.A9	48	o	No representations available
2.A9	56	+	No representations available
2.A9	112	+	No representations available
2.A9	120	o	No representations available
2.A9	160	+	No representations available
2.A9	168	o	No representations available
2.A9	224	+	No representations available

Notes

Element xxyxyy is in class 15A.

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