Overview of the GAP Character Table Library (version 1.3.10)

Character Table info for A₆.2₃

Name:

A6.2_3

Group order:

720 = 2⁴ ⋅ 3² ⋅ 5

Number of classes:

8

InfoText value:

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

Duplicates:

U3(5)M6, U3(5)M7

Maximal subgroups:

	Order	Index	Structure	Name
1	360	2	A6	A6
2	72	10	32:Q8	3^2:Q8
3	20	36	5:4	5:4
4	16	45	M11N2	M11N2

Available Brauer tables:

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

Atlas representations:

1 available

Group constructions in GAP:

AtlasGroup( "A6.2_3" ), AtlasStabilizer( "A10", "A10G1-p2520B0" ), AtlasStabilizer( "M11", "M11G1-p11B0" ), AtlasStabilizer( "M22", "M22G1-p616B0" ), AtlasSubgroup( "M11", 1 ), AtlasSubgroup( "M22", 7 ), AtlasSubgroup( "Th", 14 ), MathieuGroup( 10 ), PrimitiveGroup( 10, 6 ), PrimitiveGroup( 36, 3 ), PrimitiveGroup( 45, 2 ), SmallGroup( 720, 765 ), TransitiveGroup( 10, 31 ), TransitiveGroup( 12, 181 ), TransitiveGroup( 20, 148 ), TransitiveGroup( 20, 150 ), TransitiveGroup( 30, 162 )

Stored class fusions from this table:

3⁴:M₁₀, A₆.2², A₁₀, L₃(4).2₁, M₁₁, M₂₂, Th, U₃(5), U₄(3)

Stored class fusions to this table:

3.A₆.2₃, 3²:Q₈, 3⁴:M₁₀, 3⁵:M₁₀, 4.A₆.2₃, 5:4, 12.A₆.2₃, (2.D₁₀ × A₆).2, (2 × A₆).2₃, (4 × A₆).2₃, (A₆ × 2.A₅).2, (D₁₀ × A₆).2, (A₆ × A₅).2, A₆, M₁₁N2, (3²:4 × A₆).2

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