Overview of the GAP Character Table Library (version 1.3.10)

Character Table info for U₄(2).2

Name:

U4(2).2

Group order:

51840 = 2⁷ ⋅ 3⁴ ⋅ 5

Number of classes:

25

InfoText value:

origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5], constructions: Aut(U4(2)), GO(-1,6,2), PGO(-1,6,2), SO(-1,6,2), PSO(-1,6,2)

Duplicates:

L4(3)M4, U4(3).2_1M4

Maximal subgroups:

	Order	Index	Structure	Name
1	25920	2	U4(2)	U4(2)
2	1920	27	24:S5	mo62
3	1440	36	S6 × 2	S6x2
4	1296	40	3(1+2)+:2S4	3^(1+2)+:2S4
5	1296	40	33:(S4 × 2)	s3wrs3
6	1152	45	W(F4)	w(f4)

Stored Sylow p normalizers:

p	Order	Index	Structure	Name
5	40	1296	2 × 5:4	2x5:4

Available Brauer tables:

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

Atlas representations:

11 available

Group constructions in GAP:

AtlasGroup( "U4(2).2" ), AtlasStabilizer( "S6(2)", "S62G1-p28B0" ), AtlasSubgroup( "S6(2)", 1 ), AutomorphismGroup( AtlasGroup( "U4(2)" ) ), PSO( 5, 3 ), PrimitiveGroup( 27, 13 ), PrimitiveGroup( 36, 9 ), PrimitiveGroup( 40, 2 ), PrimitiveGroup( 40, 4 ), PrimitiveGroup( 45, 5 ), TransitiveGroup( 27, 1161 )

Stored class fusions from this table:

2⁶:U₄(2).2, 3⁵:U₄(2):2, L₄(3), S₄ × U₄(2).2, S₆(2), U₄(3).2₁, U₅(3)

Stored class fusions to this table:

2.U₄(2).2, 2⁶.U₄(2).2, 2⁶:U₄(2).2, 2¹⁺⁶₋.U₄(2).2, 2 × 5:4, 3³.S₄, 3³:(S₃ × 2), 3⁵:U₄(2):2, 3⁽¹⁺²⁾⁺:2S₄, (2 × 2¹⁺⁸):(U₄(2):2 × 2), (2 × 2¹⁺⁸):U₄(2):2, (A₄ × U₄(2)):2, (A₅ × U₄(2)):2, Isoclinic(2.U₄(2).2), S₆ × 2, U₄(2), 2⁴:S₅, 2⁴:S₄, 3³:(S₄ × 2), W(F₄)

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