Overview of the GAP Character Table Library (version 1.3.10)

Character Table info for L₃(2).2

Name:

L3(2).2

Group order:

336 = 2⁴ ⋅ 3 ⋅ 7

Number of classes:

9

InfoText value:

origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7], constructions: Aut(L3(2))

Duplicates:

L3(7)M4, L3(7)M5

Maximal subgroups:

	Order	Index	Structure	Name
1	168	2	L3(2)	L3(2)
2	42	8	7:6	7:6
3	16	21	D16	D16
4	12	28	S3 × 2	S3x2

Available Brauer tables:

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

Atlas representations:

21 available

Group constructions in GAP:

AtlasGroup( "L3(2).2" ), AtlasStabilizer( "J2", "J2G1-p1800B0" ), AtlasStabilizer( "L3(8).2", "L38d2G1-p98112B0" ), AtlasStabilizer( "U3(5).2", "U35d2G1-p750B0" ), AtlasStabilizer( "U3(7)", "U37G1-p16856B0" ), AtlasSubgroup( "J2", 7 ), AtlasSubgroup( "ON.2", 10 ), AtlasSubgroup( "U3(5).2", 6 ), AtlasSubgroup( "U3(7)", 4 ), AutomorphismGroup( AtlasGroup( "L3(2)" ) ), PrimitiveGroup( 8, 5 ), PrimitiveGroup( 21, 1 ), PrimitiveGroup( 28, 1 ), SmallGroup( 336, 208 ), TransitiveGroup( 8, 43 ), TransitiveGroup( 14, 16 ), TransitiveGroup( 16, 713 ), TransitiveGroup( 21, 20 ), TransitiveGroup( 24, 707 ), TransitiveGroup( 28, 42 ), TransitiveGroup( 28, 46 )

Stored class fusions from this table:

S₈, J₂, L₃(4).2₁, L₃(4).2₃, L₃(7), L₃(8).2, O₈⁻(2).2, ON.2, U₃(3).2, U₃(5).2, U₃(7)

Stored class fusions to this table:

2.L₃(2).2, 7:6, (2.A₇ × L₂(7)).2, (2 × L₃(2)).2, (7:3 × L₂(7)):2, (7²:(3 × 2A₄) × L₂(7)).2, (A₇ × L₂(7)):2, (L₃(2) × L₃(2)):2, (L₃(2) × S₄(4):2).2, D₁₆, Isoclinic(2.L₃(2).2), L₃(2), S₃ × 2

File created automatically by GAP on 20-May-2025.