Generators and Representations for G = L₄(4)

Standard generators

• Standard generators of L₄(4) are a and b where a is in class 2B, b is in class 4A and ab has order 30. (Source: thesis)

BBOX programs

• Finder for L₄(4)
• Checker for L₄(4)
• CCL rep tester for L₄(4)

Representations

Representation genus			Representations available			Test results		Miscellaneous information
Group	Dim	Ind	File	Char	Ring	Checker	CCL	Sparsity	Max	Size (Kb)	Comments
L4(4)	84	+	84	χ2	Z			98%	1	29.7	perm rep on 85 pts; standard generators this time!
L4(4)	85	o	85(a)	χ3	Z(ω)			98%		30.2	perm rep on 255 pts
			85(b)	χ4	Z(ω)			98%		30.2	perm rep on 255 pts
L4(4)	189	+	189(a)	χ5	C			79%		1692.1	Galois conjugate of χ6
			189(b)	χ6	C			79%		1692.2	perm rep on 1008 pts
			378	χ5+χ6	Z			76%	438	666.5	perm rep on 1008 pts (cosets of S4(4))

Notes

We assume xy is in class 30A.

The character table of L₄(4) in our version of GAP has not been sorted by dimension. We believe this to be a mistake, It may have been fixed in later editions. We have numbered our characters in order of dimension as usual:

• χ₂ is the 2nd character in the GAP table.
• χ₃ is the 51st character in the GAP table. On 30A, it has character value E(3)=(-1+Sqrt(-3))/2
• χ₄ is the 60th character in the GAP table. On 30A, it has character value E(3)² = (-1-Sqrt(-3))/2
• χ₅ is the 52nd character in the GAP table. On 30A, it has character value E(5)²+E(5)³=b5*
• χ₆ is the 63rd character in the GAP table. On 30A, it has character value E(5)+E(5)⁴=b5

Last generated on Sat Sep 24 18:53:04 2005