Generators and Representations for G = L₃(8)

Standard generators

• Standard generators of L₃(8) are a and b where a has order 2, b has order 3 and ab has order 21. (Source: ATLAS)

BBOX programs

• Finder for L₃(8)
• Checker for L₃(8)
• CCL rep tester for L₃(8)

Representations

Representation genus			Representations available			Test results		Miscellaneous information
Group	Dim	Ind	File	Char	Ring	Checker	CCL	Sparsity	Max	Size (Kb)	Comments
L3(8)	72	+	72	χ2	Z			97%	1	22.0	perm rep on 73 pts, right generators this time.
L3(8)	73	o	73(a)	χ3	C			98%		22.6	Galois conjugate of χ6
			73(b)	χ4	C			98%		22.6	Galois conjugate of χ6
			73(c)	χ5	C			98%		22.6	Galois conjugate of χ6
			73(d)	χ6	C			98%		22.6	perm rep on 511 pts
			73(e)	χ7	C			98%		22.6	Galois conjugate of χ6
			73(f)	χ8	C			98%		22.6	Galois conjugate of χ6

Notes

Element xy is in class 21A (it is conjugate to the 15th power of the 63A element listed in the Web Atlas).

N.B. The class representatives in the Web Atlas do not seem to be consistent.

Last generated on Sat Sep 24 18:53:02 2005