Generators and Representations for G = L₂(7)

Standard generators

• Standard generators of L₂(7) = L₃(2) are a and b where a has order 2, b has order 3 and ab has order 7. (Source: ATLAS)
• Standard generators of the double cover 2.L₂(7) = SL₂(7) = 2.L₃(2) are preimages A and B where B has order 3 and AB has order 7. (Source: ATLAS)

BBOX programs

• Finder for L₂(7)
• Checker for L₂(7)
• CCL rep tester for L₂(7)

Representations

Representation genus			Representations available			Test results		Miscellaneous information
Group	Dim	Ind	File	Char	Ring	Checker	CCL	Sparsity	Max	Size (Kb)	Comments
L2(7)	3	o	3(a)	χ2	C			55%		0.5	perm rep on 42 pts
			3(b)	χ3	C			55%		0.5	perm rep on 42 pts
			6(a)	χ2+χ3	Z			77%	1	0.7	perm rep on 42 pts (cyclic-4)
L2(7)	6	+	6(b)	χ4	Z			76%	1	0.7	perm rep on 7 pts
L2(7)	7	+	7	χ5	Z			79%	1	0.8	perm rep on 8 pts
L2(7)	8	+	8	χ6	Z			79%	1	0.8	induce from Borel, reseed
2.L2(7)	4	o	No representations available
2.L2(7)	6	-	No representations available
2.L2(7)	8	-	No representations available

Last generated on Sat Sep 24 18:52:55 2005