Generators and Representations for G = L₂(8)

Standard generators

• Standard generators of L₂(8) are a and b where a has order 2, b has order 3 and ab has order 7. (Source: ATLAS)

BBOX programs

• Finder for L₂(8)
• Checker for L₂(8)
• CCL rep tester for L₂(8)

Representations

Representation genus			Representations available			Test results		Miscellaneous information
Group	Dim	Ind	File	Char	Ring	Checker	CCL	Sparsity	Max	Size (Kb)	Comments
L2(8)	7	+	7(a)	χ2	Z			73%	1	0.8	perm rep on 56 pts
			7(b)	χ3	C			73%		1.1	Galois conjugate of χ5
			7(c)	χ4	C			73%		1.1	Galois conjugate of χ5
			7(d)	χ5	C			73%		1.2	perm rep on 56 pts
L2(8)	8	+	8	χ6	Z			76%	1	0.8	perm rep on 9 pts
L2(8)	9	+	9(a)	χ7	C			74%		1.7	perm rep on 28 pts, one of the 9abc reps
			9(b)	χ8	C			74%		1.7	Galois conjugate of χ7
			9(c)	χ9	C			74%		1.7	Galois conjugate of χ7

Last generated on Sat Sep 24 18:52:56 2005