Overview of the GAP Character Table Library (version 1.3.10)

Character Table info for 3.A₆

Name:

3.A6

Group order:

1080 = 2³ ⋅ 3³ ⋅ 5

Number of classes:

17

InfoText value:

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

Duplicates:

3.L3(4)M4, 3.L3(4)M5

Maximal subgroups:

	Order	Index	Structure	Name
1	180	6	3 × A5	3xA5
2	180	6	3 × A5	3.A6M2
3	108	10	31+2:4	3^(1+2):4
4	72	15	3 × S4	3xSymm(4)
5	72	15	3 × S4	3.A6M5

Stored Sylow p normalizers:

p	Order	Index	Structure	Name
2	24	45	3 × D8	3xD8
3	108	10	31+2:4	3^(1+2):4
5	30	36	3 × D10	3xD10

Available Brauer tables:

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

Atlas representations:

20 available

Group constructions in GAP:

AtlasGroup( "3.A6" ), AtlasSubgroup( "3.A6.2_1", 1 ), AtlasSubgroup( "3.A7", 1 ), AtlasSubgroup( "3.L3(4)", 3 ), PerfectGroup( 1080, 1 ), SmallGroup( 1080, 260 ), TransitiveGroup( 18, 262 )

Stored class fusions from this table:

3.A₆.2₁, 3.A₆.2₂, 3.A₆.2₃, 3.A₇, 3.L₃(4), A₆

Stored class fusions to this table:

(2.2⁴.2⁶):3A₆, 2⁴⁺⁶:3A₆, 3 × A₅, 3 × S₄, 2⁴:3A₆, 3¹⁺²:4, 3 × A₅, 3 × D₈, 3 × D₁₀, 3 × S₄, 6.A₆, 2⁵:3A₆, 2.2⁵:3A₆, Isoclinic(6.A₆ × 2)

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