Generators and Representations for G = L₂(27)

Standard generators

• Standard generators of L₂(27) 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(27) = SL₂(27) are preimages A and B where B has order 3 and AB has order 7. (Source: ATLAS)

BBOX programs

• Finder for L₂(27)
• Checker for L₂(27)
• CCL rep tester for L₂(27)

Representations

Representation genus			Representations available			Test results		Miscellaneous information
Group	Dim	Ind	File	Char	Ring	Checker	CCL	Sparsity	Max	Size (Kb)	Comments
L2(27)	13	o	13(a)	χ2	Z(ω)			77%		1.3	perm rep on 351 pts
			13(b)	χ3	Z(ω)			77%		1.3	perm rep on 351 pts
			26(g)	χ2+χ3	Z			81%	10	3.4	perm rep on 351 pts
L2(27)	26	+	78(a)	χ4+χ5+χ6	Z			64%	19	27.9	perm rep on 702 pts (cosets of D14)
L2(27)	27	+	27	χ10	Z			92%	1	3.6	perm rep on 27 pts
L2(27)	28	+	28(a)	χ11	C			96%		4.0	induce from Borel
			28(b)	χ12	C			96%		4.0	induce from Borel
			28(c)	χ13	C			96%		4.0	induce from Borel
			28(d)	χ14	C			96%		4.0	induce from Borel
			28(e)	χ15	C			96%		4.0	induce from Borel
			28(f)	χ16	C			96%		4.0	induce from Borel
2.L2(27)	14	o	No representations available
2.L2(27)	26	-	No representations available
2.L2(27)	28	-	No representations available

Notes

Identifying classes: 13D is ababb.

Last generated on Sat Sep 24 18:52:59 2005