Generators and Representations for G = A₆

Standard generators

• Standard generators of A₆ are a and b where a has order 2, b has order 4 and ab has order 5. (Source: ATLAS)
• Standard generators of the double cover 2.A₆ = SL₂(9) are preimages A and B where AB has order 5 and ABB has order 5. (Source: ATLAS)
• Standard generators of the triple cover 3.A₆ are preimages A and B where A has order 2 and B has order 4. (Source: ATLAS)
• Standard generators of the sixfold cover 6.A₆ are preimages A and B where A has order 4, AB has order 15 and ABB has order 5. (Source: ATLAS)

BBOX programs

• Checker for A₆
• CCL rep tester for A₆

Representations

Representation genus			Representations available			Test results		Miscellaneous information
Group	Dim	Ind	File	Char	Ring	Checker	CCL	Sparsity	Max	Size (Kb)	Comments
A6	5	+	5(a)	χ2	Z			64%	1	0.5	young rep 21111
			5(b)	χ3	Z			60%	1	0.5	young rep 222
A6	8	+	8(a)	χ4	C			69%		1.0	change basis with null-vector of a+b^2+ab^2-3
			8(b)	χ5	C			69%		0.9	Galois conjugate of χ4
A6	9	+	9	χ6	Z			73%	1	0.8	young rep 2211
A6	10	+	10	χ7	Z			78%	1	0.9	young rep 411
2.A6	4	-	4(a)	χ8	Z(ω)			43%		0.5	clifford.g
2.A6	8	-	No representations available
2.A6	10	-	No representations available
3.A6	3	o	3(a)	χ14	C			55%		0.5	spin up with a 5-elt, writable over Z(w15)
3.A6	6	o	6	χ16	Z(ω)			83%		0.6	monomial representation of some description
3.A6	9	o	9	χ17	Z(ω)			72%		0.9	perm rep on 45 pts
3.A6	15	o	15	χ18	C			81%		1.8	tensor 3 with 5
6.A6	6	o	6(a)	χ19	C			65%		1.4	seeded with -E(8) espace of b
6.A6	12	o	12(a)	χ21	C			75%		1.4	tensor 3(3A6) with 4(2A6)

Notes

The element xy is in class 5A.

Last generated on Sat Sep 24 18:52:46 2005