Generators and Representations for G = U₃(5)

Standard generators

• Standard generators of U₃(5) are a and b where a has order 3, b is in class 5A and ab has order 7. (Source: ATLAS)
• Standard generators of 3.U₃(5) are preimages A and B where B has order 5 and AB has order 7. (Source: ATLAS)

BBOX programs

• Checker for U₃(5)
• CCL rep tester for U₃(5)

Representations

Representation genus			Representations available			Test results		Miscellaneous information
Group	Dim	Ind	File	Char	Ring	Checker	CCL	Sparsity	Max	Size (Kb)	Comments
U3(5)	20	-	20	χ2	C			56%		45.3	REPSN package
U3(5)	21	+	21	χ3	Z			82%	2	2.5	perm rep on 50a pts
U3(5)	28	+	28(a)	χ4	Z			84%	3	3.9	perm rep on 50c pts
			28(b)	χ5	Z			81%	3	3.9	perm rep on 50b pts
			28(c)	χ6	Z			86%	2	3.8	perm rep on 50a pts
U3(5)	84	+	84	χ7	Z			59%	67	33.5	perm rep on 525 pts, LLL'ed
U3(5)	105	+	105	χ8	Z			94%	2	46.6	perm rep on 252 pts
U3(5)	125	+	125	χ9	Z			98%	1	64.7	perm rep on 126 pts
U3(5)	126	+	126(a)	χ10	Z			54%	150	79.1	perm rep on 525 pts, LLL'ed
U3(5)	126	o	252	χ11+χ12	Z			64%	499	314.4	perm rep on 1050(a) pts
U3(5)	144	o	288	χ13+χ14	Z			57%	1393	450.6	perm rep on 750 pts
3.U3(5)	21	o	21(a)	χ17	Q(ω)			59%		7.0	restrict 63-dim Weil rep of S6(5) and split. Possibly χ18?
3.U3(5)	48	o	No representations available
3.U3(5)	84	o	No representations available
3.U3(5)	105	o	No representations available
3.U3(5)	126	o	No representations available
3.U3(5)	144	o	No representations available

Last generated on Sat Sep 24 18:53:07 2005