Generators and Representations for G = L₃(4)

Standard generators

• Standard generators of L₃(4) are a and b where a has order 2, b has order 4, ab has order 7 and abb has order 5. (Source: ATLAS)
• Standard generators of the triple cover 3.L₃(4) are preimages A and B where A has order 2 and B has order 4. (Source: ATLAS)
• Standard generators of the double cover 2.L₃(4) are preimages A and B where AB has order 7, ABB has order 5 and ABABABBB has order 5. (Source: ATLAS)
• Standard generators of the quadruple cover 4a.L₃(4) are preimages A and B where B has order 4, AB has order 7 and ABB has order 5. (Source: ATLAS)
• Standard generators of the quadruple cover 4b.L₃(4) are preimages A and B where B has order 4, AB has order 7 and ABB has order 5. (Source: ATLAS)
• Standard generators of the sextuple cover 6.L₃(4) are preimages A and B where AB has order 2, B has order 4, AB has order 21, ABB has order 5 and ABABABBB has order 5. (Source: ATLAS)
• Standard generators of the twelvefold cover 12a.L₃(4) are preimages A and B where A has order 2, B has order 4, AB has order 21 and ABB has order 5. (Source: ATLAS)
• Standard generators of the twelvefold cover 12b.L₃(4) are preimages A and B where A has order 2, B has order 4, AB has order 21 and ABB has order 5. (Source: ATLAS)

BBOX programs

• Finder for L₃(4)
• Checker for L₃(4)
• CCL rep tester for L₃(4)

Representations

Representation genus			Representations available			Test results		Miscellaneous information
Group	Dim	Ind	File	Char	Ring	Checker	CCL	Sparsity	Max	Size (Kb)	Comments
L3(4)	20	+	20	χ2	Z			92%	1	2.1	perm rep on 21 pts
L3(4)	35	+	35(a)	χ3	Z			94%	1	5.6	perm reps on 56 pts
			35(b)	χ4	Z			92%	3	5.7	perm reps on 56 pts
			35(c)	χ5	Z			92%	2	5.7	perm reps on 56 pts
L3(4)	45	o	45(a)	χ6	C			84%		14.8	perm char 280
			45(b)	χ7	C			84%		14.9	complex conjugate
L3(4)	63	+	63(a)	χ8	C			98%		17.0	perm rep on 252
			63(b)	χ9	C			98%		17.0	Galois conjugate of χ8
L3(4)	64	+	64	χ10	Z			81%	5	18.0	perm rep on 120, LLL'ed
2.L3(4)	10	o	No representations available
2.L3(4)	28	+	No representations available
2.L3(4)	36	+	No representations available
2.L3(4)	64	+	No representations available
2.L3(4)	70	+	No representations available
2.L3(4)	90	+	No representations available
3.L3(4)	15	o	No representations available
3.L3(4)	21	o	No representations available
3.L3(4)	45	o	No representations available
3.L3(4)	63	o	No representations available
3.L3(4)	84	o	No representations available
41.L3(4)	8	o	No representations available
42.L3(4)	20	o	No representations available
42.L3(4)	28	o	No representations available
42.L3(4)	36	o	No representations available
41.L3(4)	56	o	No representations available
42.L3(4)	64	o	No representations available
41.L3(4)	64	o	No representations available
41.L3(4)	80	o	No representations available
42.L3(4)	80	o	No representations available
6.L3(4)	6	o	No representations available
6.L3(4)	36	o	No representations available
6.L3(4)	42	o	No representations available
6.L3(4)	60	o	No representations available
6.L3(4)	90	o	No representations available
121.L3(4)	24	o	No representations available
122.L3(4)	36	o	No representations available
121.L3(4)	48	o	No representations available
122.L3(4)	48	o	No representations available
122.L3(4)	60	o	No representations available
122.L3(4)	84	o	No representations available
121.L3(4)	120	o	No representations available

Notes

Class reps: y is 4A, xyxy³xy² is 4B, xyxy²xy³ is 4C (arbitrary choice).

Last generated on Sat Sep 24 18:53:01 2005