Generators and Representations for G = A₇

Standard generators

• Standard generators of A₇ are a and b where a is in class 3A, b has order 5 and ab has order 7. (Source: ATLAS)
• Standard generators of the double cover 2.A₇ are preimages A and B where A has order 3, B has order 5 and AB has order 7. Any two of these conditions implies the third. (Source: ATLAS)
• Standard generators of the triple cover 3.A₇ are preimages A and B where B has order 5 and AB has order 7. (Source: ATLAS)
• Standard generators of the sextuple cover 6.A₇ are preimages A and B where B has order 5 and AB has order 7. (Source: ATLAS)

BBOX programs

• Finder for A₇
• Checker for A₇
• CCL rep tester for A₇

Representations

Representation genus			Representations available			Test results		Miscellaneous information
Group	Dim	Ind	File	Char	Ring	Checker	CCL	Sparsity	Max	Size (Kb)	Comments
A7	6	+	6	χ2	Z			76%	1	0.6	young rep 61
A7	10	o	10(a)	χ3	C			50%		1.4	splitting Young representation with χSpin (based on +1-espace of AB)
			10(b)	χ4	C			50%		1.4	complex conjugate of χ3
			20	χ3+χ4	Z			91%	1	2.1	young rep 4111
A7	14	+	14(a)	χ5	Z			85%	1	1.3	young rep 52
			14(b)	χ6	Z			81%	1	1.3	young rep 43
A7	15	+	15	χ7	Z			88%	1	1.4	young rep 511
A7	21	+	21	χ8	Z			86%	1	2.3	young rep 331
A7	35	+	35	χ9	Z			92%	1	5.7	young rep 421
2.A7	4	o	No representations available
2.A7	14	-	No representations available
2.A7	20	-	No representations available
2.A7	36	-	No representations available
3.A7	6	o	No representations available
3.A7	15	o	No representations available
3.A7	21	o	No representations available
3.A7	24	o	No representations available
6.A7	6	o	No representations available
6.A7	24	o	No representations available
6.A7	36	o	No representations available

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