Overview of the GAP Character Table Library (version 1.3.8)

Character Table info for A₆

Name:

A6

Group order:

360 = 2³ ⋅ 3² ⋅ 5

Number of classes:

7

InfoText value:

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

Duplicates:

A₆, A₆

Maximal subgroups:

	Order	Index	Structure	Name
1	60	6	A5	A5
2	60	6	A5	A6M2
3	36	10	32:4	3^2:4
4	24	15	S4	s4
5	24	15	S4	A6M5

Stored Sylow p normalizers:

p	Order	Index	Structure	Name
2	8	45	D8	D8
3	36	10	32:4	3^2:4
5	10	36	D10	D10

Available Brauer tables:

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

Atlas representations:

26 available

Group constructions in GAP:

AlternatingGroup( 6 ), AtlasGroup( "A6" ), AtlasStabilizer( "A7", "A7G1-p7B0" ), AtlasStabilizer( "L3(4)", "L34G1-p56aB0" ), AtlasStabilizer( "L3(4)", "L34G1-p56bB0" ), AtlasStabilizer( "L3(4)", "L34G1-p56cB0" ), AtlasSubgroup( "A6.2_1", 1 ), AtlasSubgroup( "A7", 1 ), AtlasSubgroup( "L3(4)", 3 ), AtlasSubgroup( "L3(4)", 4 ), AtlasSubgroup( "L3(4)", 5 ), AtlasSubgroup( "S4(5)", 8 ), PSL( 2, 9 ), PerfectGroup( 360, 1 ), PrimitiveGroup( 6, 3 ), PrimitiveGroup( 10, 3 ), PrimitiveGroup( 15, 2 ), SmallGroup( 360, 118 ), TransitiveGroup( 6, 15 ), TransitiveGroup( 10, 26 ), TransitiveGroup( 15, 20 ), TransitiveGroup( 20, 89 ), TransitiveGroup( 30, 88 )

Stored class fusions from this table:

2⁴:A₆, 3⁴:A₆, S₆, A₆.2₂, A₆.2₃, A₇, L₃(4), S₄(5), U₃(11)

Stored class fusions to this table:

2.A₆, 2⁵:A₆, 2⁴:A₆, 2⁵:A₆, 3.A₆, 3²:4, 3⁴:A₆, 2.2⁵:A₆, 6.A₆, A₅, A₅, S₄, D₈, D₁₀, 2⁵:A₆, P21/G1/L1/V1/ext3, P21/G1/L1/V1/ext4, P21/G1/L3/V2/ext3, P21/G2/L1/V1/ext2, P21/G2/L1/V2/ext2, P21/G2/L1/V3/ext2, P21/G2/L2/V1/ext2, P21/G2/L2/V2/ext2, P21/G2/L2/V3/ext2, P21/G2/L5/V2/ext2, P21/G3/L2/V1/ext2, P21/G3/L5/V1/ext2, S₄

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