Overview of the GAP Character Table Library (version 1.3.8)

Character Table info for S₆

Name:

A6.2_1

Group order:

720 = 2⁴ ⋅ 3² ⋅ 5

Number of classes:

11

InfoText value:

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

Maximal subgroups:

	Order	Index	Structure	Name
1	360	2	A6	A6
2	120	6	S5	A5.2
3	120	6	S5	A6.2_1M3
4	72	10	32:D8	s3wrs2
5	48	15	2 × S4	2xSymm(4)
6	48	15	S4 × 2	s2wrs3

Available Brauer tables:

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

Atlas representations:

5 available

Group constructions in GAP:

AtlasGroup( "A6.2_1" ), AtlasStabilizer( "A7.2", "S7G1-p7B0" ), AtlasStabilizer( "U4(2)", "U42G1-p36B0" ), AtlasSubgroup( "A7.2", 2 ), AtlasSubgroup( "S4(4)", 7 ), POmega( 5, 2 ), PSp( 4, 2 ), PrimitiveGroup( 6, 4 ), PrimitiveGroup( 10, 5 ), PrimitiveGroup( 15, 3 ), SmallGroup( 720, 763 ), SymmetricGroup( 6 ), TransitiveGroup( 6, 16 ), TransitiveGroup( 10, 32 ), TransitiveGroup( 12, 183 ), TransitiveGroup( 15, 28 ), TransitiveGroup( 20, 145 ), TransitiveGroup( 20, 149 ), TransitiveGroup( 30, 164 ), TransitiveGroup( 30, 166 ), TransitiveGroup( 30, 176 )

Stored class fusions from this table:

A₆.2², S₇, A₈, L₃(4).2₂, S₄(4), U₄(2)

Stored class fusions to this table:

2.2⁴.S₆, 2.A₆.2₁, 2⁴.S₆, 2⁵:S₆, 2⁶:S₆, 2³⁺⁸:(S₃ × S₆), 2 × S₄, 3.A₆.2₁, 3⁴:S₆, 5:4, 6.A₆.2₁, (3²:4 × A₆).2, (3²:8 × A₆).2, (3¹⁺²:4 × A₆).2, (3¹⁺²:8 × A₆).2, (3 × A₆).2₁, (4 × A₆):2, (A₆ × A₄):2, (A₆ × A₅):2, (A₆ × U₃(3)):2, (A₇ × A₆):2, S₅, A₆, S₅, D₈ × 2, 2⁴:S₆, S₄ × 2, 3²:D₈, suzdx

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