Generators and Representations for G = A₈

Standard generators

• Standard generators of A₈ are a and b where a is in class 3A, b has order 7, ab has order 6 and abb has order 15. (Source: ATLAS)
• Standard generators of the double cover 2.A₈ are preimages A and B where A has order 3 and B has order 7. (Source: ATLAS)

BBOX programs

• Finder for A₈
• Checker for A₈
• CCL rep tester for A₈

Representations

Representation genus			Representations available			Test results		Miscellaneous information
Group	Dim	Ind	File	Char	Ring	Checker	CCL	Sparsity	Max	Size (Kb)	Comments
A8	7	+	7	χ2	Z			79%	1	0.6	Young rep 71
A8	14	+	14	χ3	Z			78%	1	1.3	Young rep 44
A8	20	+	20	χ4	Z			87%	1	2.1	Young rep 62
A8	21	+	21(a)	χ5	Z			91%	1	2.3	Young rep 611
A8	21	o	21(b)	χ6	C			3%		79.2	rho-split Young rep
			21(c)	χ7	C			3%		79.2	complex conjugate of χ6
			42	χ6+χ7	Z			89%	2	8.0	Young rep 332
A8	28	+	28	χ8	Z			87%	1	3.7	Young rep 53
A8	35	+	35	χ9	Z			94%	1	5.6	Young rep 5111
A8	45	o	45(a)	χ10	C			4%		50.3	rho-split Young rep
			45(b)	χ11	C			4%		50.3	complex conjugate of χ10
			90	χ10+χ11	Z			95%	1	34.0	Young rep 4211
A8	56	+	56	χ12	Z			92%	2	13.6	Young rep 422
A8	64	+	64	χ13	Z			93%	1	17.5	Young rep 521
A8	70	+	70	χ14	Z			93%	2	21.1	Young rep 431
2.A8	8	+	8	χ15	Z			77%	1	0.8	clifford.g, seeded with null vector of a^2+b+a^2b^3+i
2.A8	24	o	24(a)	χ16	C			70%		5.0	split 7 x 8
2.A8	48	-	No representations available
2.A8	56	o	No representations available
2.A8	64	-	No representations available

Notes

Element y is in class 7A and xy² is in class 15A.

Last generated on Sat Sep 24 18:52:47 2005