Generators and Representations for G = U₄(3)

Standard generators

• Standard generators of U₄(3) are a and b where a has order 2, b is in class 6A, ab has order 7 and abababbababb has order 5.
• Standard generators of the double cover 2.U₄(3) are preimages A and B where B has order and AB has order (?) .(Source: ATLAS)

BBOX programs

• Checker for U₄(3)
• CCL rep tester for U₄(3)

Representations

Representation genus			Representations available			Test results		Miscellaneous information
Group	Dim	Ind	File	Char	Ring	Checker	CCL	Sparsity	Max	Size (Kb)	Comments
U4(3)	21	+	21	χ2	Z			90%	1	2.4	perm rep on 112 pts
U4(3)	35	+	35(a)	χ3	Z			90%	2	5.8	perm rep on 126 pts
			35(b)	χ4	Z			90%	2	5.8	perm rep on 126 pts
U4(3)	90	+	90	χ5	Z			94%	2	34.2	perm rep on 112 pts
U4(3)	140	+	140	χ6	Z			96%	2	81.7	perm rep on 162 pts
U4(3)	189	+	189	χ7	Z			95%	3	148.2	perm rep on 280 pts
U4(3)	210	+	210	χ8	Z			78%	40	192.4	perm rep on 540 pts
2.U4(3)	20	-	No representations available
2.U4(3)	56	+	No representations available
2.U4(3)	70	+	No representations available
2.U4(3)	70	o	No representations available
2.U4(3)	120	+	No representations available
2.U4(3)	210	o	No representations available
4.U4(3)	20	o	No representations available
4.U4(3)	120	o	No representations available
4.U4(3)	140	o	No representations available
4.U4(3)	224	o	No representations available
122.U4(3)	36	o	No representations available
121.U4(3)	84	o	No representations available
121.U4(3)	120	o	No representations available
121.U4(3)	216	o	No representations available
122.U4(3)	216	o	No representations available

Notes

We assume xyxy⁵xy² is in 6B and xyxy²xy⁵ is in 6C.

Last generated on Sat Sep 24 18:53:10 2005