Overview of the GAP Character Table Library (version 1.3.8)

Character Table info for L₃(4)

Name:

L3(4)

Group order:

20160 = 2⁶ ⋅ 3² ⋅ 5 ⋅ 7

Number of classes:

10

InfoText value:

origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]

Maximal subgroups:

	Order	Index	Structure	Name
1	960	21	24:A5	2^4:A5
2	960	21	24:A5	2^4:A5
3	360	56	A6	A6
4	360	56	A6	L3(4)M4
5	360	56	A6	L3(4)M5
6	168	120	L3(2)	L3(2)
7	168	120	L3(2)	L3(4)M7
8	168	120	L3(2)	L3(4)M8
9	72	280	32:Q8	3^2:Q8

Stored Sylow p normalizers:

p	Order	Index	Structure	Name
2	192	105	24:A4b	2^4:A4b
3	72	280	32:Q8	3^2:Q8
5	10	2016	D10	D10
7	21	960	7:3	7:3

Available Brauer tables:

p
2	dec. matrix (PDF)
3	dec. matrix (PDF)
5	dec. matrix (PDF)
7	dec. matrix (PDF)

Atlas representations:

48 available

Group constructions in GAP:

AtlasGroup( "L3(4)" ), AtlasStabilizer( "M22", "M22G1-p22B0" ), AtlasSubgroup( "M22", 1 ), PSL( 3, 4 ), PerfectGroup( 20160, 5 ), PrimitiveGroup( 21, 4 ), PrimitiveGroup( 56, 1 ), PrimitiveGroup( 120, 6 ), PrimitiveGroup( 280, 3 ), TransitiveGroup( 21, 67 )

Stored class fusions from this table:

2⁹.L₃(4), L₃(4).2₁, L₃(4).2₂, L₃(4).2₃, L₃(4).3, L₃(4).6, M₂₂, U₄(3)

Stored class fusions to this table:

2.L₃(4), 2¹⁰:L₃(4), 2².L₃(4), 2¹⁰:2.L₃(4), 2⁴:A₄b, 2⁴:A₅, 2⁹.L₃(4), 3.L₃(4), 3²:Q₈, 4₁.L₃(4), 4₂.L₃(4), 6.L₃(4), 7:3, 12₁.L₃(4), 12₂.L₃(4), (2² × 3).L₃(4), A₆, D₁₀, L₃(2), A₆, A₆, L₃(2), L₃(2), L₃(4)Syl₂

File created automatically by GAP on 13-Mar-2024.