Overview of the GAP Character Table Library (version 1.3.10)

Character Table info for U₃(3).2

Name:

U3(3).2

Group order:

12096 = 2⁶ ⋅ 3³ ⋅ 7

Number of classes:

16

InfoText value:

origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7], constructions: Aut(U3(3))

Duplicates:

G2(3)M2

Maximal subgroups:

	Order	Index	Structure	Name
1	6048	2	U3(3)	U3(3)
2	432	28	31+2:SD16	3^(1+2):SD16
3	336	36	L3(2).2	L3(2).2
4	192	63	21+4.S3	2^(1+4).S3
5	192	63	42:D12	4^2:D12

Available Brauer tables:

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

Atlas representations:

9 available

Group constructions in GAP:

AtlasGroup( "U3(3).2" ), AtlasStabilizer( "G2(4)", "G24G1-p20800B0" ), AtlasStabilizer( "J2.2", "J2d2G1-p100B0" ), AtlasStabilizer( "S6(2)", "S62G1-p120B0" ), AtlasSubgroup( "3D4(2)", 3 ), AtlasSubgroup( "G2(3)", 1 ), AtlasSubgroup( "G2(3)", 2 ), AtlasSubgroup( "G2(4)", 6 ), AtlasSubgroup( "G2(5)", 6 ), AtlasSubgroup( "J2.2", 2 ), AtlasSubgroup( "S6(2)", 4 ), AutomorphismGroup( AtlasGroup( "U3(3)" ) ), PrimitiveGroup( 28, 5 ), PrimitiveGroup( 36, 7 ), PrimitiveGroup( 63, 2 ), PrimitiveGroup( 63, 4 ), TransitiveGroup( 28, 393 )

Stored class fusions from this table:

³D₄(2), F₃₊, G₂(3), G₂(4), G₂(5), J₂.2, S₆(2), U₄(3).2₃

Stored class fusions to this table:

2.2⁶:u₃(3):2, 2².(U₃(3).2 × S₄), (2⁶:U₃(3)):2, 2¹⁺⁴.S₃, 3¹⁺²:SD₁₆, 4²:D₁₂, 7:6, (2.A₆ × U₃(3)).2, (A₆ × U₃(3)):2, (Q₁₆ × U₃(3)).2, Isoclinic(2 × U₃(3).2), L₃(2).2, M₁₂N2, U₃(3)

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